Why is Lebesgue so often spelled "Lebesque"? Henri Lebesgue (1875-1941) was a French mathematician, best known for inventing the theory of measure and integration that bears his name.
As far as I know, "Lebesgue" is the correct spelling of his surname, but it seems to be quite common for people to spell it "Lebesque", with a q.  Why is this?


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*Is "Lebesque" somehow an acceptable variant spelling of "Lebesgue"?  (I don't really know much about French orthography.)

*Would "Lebesque" be pronounced similarly to "Lebesgue" in French?  (I don't know much about French pronunciation, either.)

*Was this an error made in some widely read book, which has thus infected many other people?

*Is it simply that the letters g and q have a similar shape in some scripts or typefaces?  I don't seem to see people  mixing up g and q very often in other contexts.

Edit. To look for further examples, I searched for "lebesque" on MathSciNet (search results, subscription required).  There are 48 matches for the term, either in article/book titles or other metadata, or in reviews.  
There seems to perhaps be a disproportionate number that are in Russian or other Eastern European languages.  Maybe there is something related to transliterations to/from Cyrillic?  They could also just be errors by the translator.
Many of them, however, turned out to be errors in the MR database.  For example, there is an item listed as "Brown, Arlen. On the Lebesque convergence theorem. Math. Nachr. 23 1961 141–148.", but when we go to the article itself, as originally published, we see it was in fact spelled Lebesgue.  So this is probably an error introduced in data entry or perhaps OCR.
Worse yet: MathSciNet has an entry for a 1927 Acta paper by Lebesgue himself, under the author "Lebesque, Henri"!  And when we follow the link to the article on SpringerLink, we see that it is also spelled "Lebesque" in the SpringerLink database.  But if we download the original article itself, it is actually spelled Lebesgue.
I didn't check all of them, but there were a few that I was able to verify:


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*Parfënov, O. G. Criteria of nuclearity of embedding operators acting between Bergman spaces and weighted Lebesque  spaces. Math. Nachr. 154 (1991), 105–115.  MR | Journal

*Abilov, V. A.; Pkhasy, S. The evaluation of the Lebesque function of Fourier-Jacobi double series.  Math. Balkanica (N.S.) 2 (1988), no. 2-3, 208–209. MR | Article

*In A Concise Introduction to the Theory of Integration by Daniel W. Stroock, Chapter III is entitled "Lebesque Integration".  See the table of contents. However, the titles of other chapters and sections use the spelling "Lebesgue", so this is probably just an unfortunate typo.
 A: Words ending in "que" are much more common than words ending in "gue". See Latin. :-)
A: I am also a native French speaker (from France) and I confirm that Lebesgue is the correct spelling and that Lebesque is just a bad typo from this site.
The situation is not that bad, however. As the OP pointed out, there are 82 users who misspelled his name, but if you search for "Lebesgue" on this site you will find 8,587 entries. So the ratio is less than 1%. By the way, I remember having corrected this typo at least once and I invite you to help me until the number of such misspellings reaches Lebesgue measure $0$....
A: 
Why is Lebesgue so often spelled “Lebesque” ?

Because “-esque” is a very common French suffix, corresponding to the English “-ish”. $($For instance, in Romanian, which is a Romance language, just like French, the equivalent “-escu” is extremely popular in family names$)$. So the confusion is quite understandable.
A: I think that the comment by the OP that this is particularly common in articles from Eastern Europe points to a possible contributing source of the confusion. Namely, Russian, Polish, and a number of other Slavic languages (not to mention German) have something called "final consonant devoicing." A consequence of this is that at the end of a word, any g sound will be pronounced as k. So for someone having only heard the name, but not having looked particularly closely at how it is written, it may be tempting to write it as Lebesque, as if it ended in a $k$ sound, particularly if they are aware that -esque is a possible ending in French names, the most common such name probably being Lévesque (in which the s is silent, just as in Lebesgue).
A: I think this is a good question, and as the edit makes clear, the scope of it is certainly larger than stackexchange websites.  
I have wondered about this myself over the years.  Nate Eldredge's suggestions are as good as any I can come up with: in particular, yes, in older typefaces "Lebesgue" and "Lebesque" look very similar.  Especially, slightly shoddy typesetting can lead to the bottom portions of these characters being removed, so I think it is likely that there is at least one classic text in which one cannot properly read the name.  It would be interesting to find one.
I will mention what I think is one further ingredient: mathematics is decidedly less concerned with supplying source material (primary or otherwise) and in correctly associating ideas with names than most other academic fields.  This is true to a degree which is simply remarkable once you notice it.  For instance, a typical undergraduate mathematics textbook does not have a bibliography!  If results are attributed to specific people, it is people like Newton, Leibniz and Cauchy, and this being done to leaven the text with human interest stories.  (It is common enough to have a footnote giving a sentence or two of biographical information about someone like Cauchy.  Which is nice, but calls into stark relief the absence of actual bibliographic information.)  
The most common amount of effort taken in tracking down the reference in which Theorem X.Y was actually proved is zero.  Rather, the association of a name to a result, when (too rarely) done in a mathematics textbook, is done entirely according to the author's whims.  This turns the association of names with results into a game of whisper down the lane played by textbook authors and their readers.
I will give another example, closer to my own heart.  For almost 20 years now I have been a fan of the Chevalley-Warning Theorem (and recently a bit more than a fan, but if there is any relevance to that, it is just that in this case I actually have read the primary literature).  Now I have noticed over the years that about 5% of the mathematical world refers to this result as the "Chevalley-Waring Theorem".  I don't think there can be any good reason -- no one calls it that after their attention is drawn to Ewald Warning's 1936 paper on the subject -- and yet I have seen it in published papers.  Most recently I saw it in a review of my recent grant application.

Finally the PI has a proposal concerning 'combinatorial nullstellensatze and Chevalley-Waring'. I read this section, but have insufficient expertise in this subject area to judge the importance of this proposal. I see that for instance the PI has generalizations of Waring's theorem (saying that a system of polynomial equations over a finite field of low degree compared to the number of variables, either has no solutions or has quite a lot of solutions) to rings of integers modulo prime powers. This seems quite striking to a non-expert. 

I think this is interesting glimpse of the psychology involved.  Needless to say the grant application spoke of the "Chevalley-Warning Theorem".  Probably the reviewer was, like many number theorists, much more familiar with the mathematician Edward Waring than the mathematician Ewald Warning, so substitutes one for the other without noticing.  Or checking.  In fact the reviewer includes quotation marks around what is by no means a direct quote (for that matter in my grant application it says Combinatorial Nullstellensätze, not combinatorial nullstellensatze, so a German language error has also been introduced inside a direct quote).  
I don't mean to be too hard on the reviewer, who openly admitted lack of expertise in the area.  They undoubtedly also had a lot of evaluative work to do in a short period of time, and getting the names of dead mathematicians right was not their priority.  But that's my point: as a profession, getting the names of dead mathematicians right is typically our lowest priority.  I think this is something to work on in the future, because it is so nicely enabled by modern technology.  Time was you'd need to make a trip to a mathematical library to convince yourself that it's Chevalley-Warning, not Chevalley-Waring.  Now, if you google Chevalley-Waring, it will show you instead results for Chevalley-Warning.  Things are not as hard as they used to be.  
P.S.: It is interesting to read the 48 MathSciNet citations to "Lebesque".  In the reviews dating back to 1973, the mistake is always corrected in the title or remarked upon by the reviewer.  Before then this seems mostly not to happen, and sometimes it is even the reviewer who introduces the mistake, as e.g. in MR0253894 from 1969.  Here is an exception:
the review of MR0179321 from 1963 is

Simples exercices sans difficulté et sans grand intérêt. (Le nom de Lebesgue est systématiquement estropié dans le titre et dans le texte.) 

The second oldest use of "Lebesque" occurs in

Lebesque, Henri
  Sur la recherche des fonctions primitives. (French)
  Acta Math. 49 (1927), no. 3-4, 245–262. 

However a look at the original paper shows that the author's surname is spelled LEBESGUE (capitals in the original).
The oldest use of "Lebesque" comes from the oldest paper I have yet seen on MathSciNet:

Lebesque, A.;
  Intégration d'un système d'équations linéaires du ne ordre. (French)
  J. Reine Angew. Math. 15 (1836), 185–190.

According to the first page of this paper, this author's name is indeed "Lebesque".  Anyway, Lebesque is a real French surname.
Final Irony: Henri Lebesgue's father was a typesetter.
A: In the French language, words ending in QUE (4503) are almost 10 times more common than words ending in GUE (583). Furthermore, that same site counts 189 French words ending in SQUE and 0 ending in SGUE. 
Some people here have said that QUE is also more common in English, but the difference in English is much less marked (381-QUE vs 240-GUE). 
Given that the name is indeed a French name I think it is natural to expect it to have the more common French ending, especially since many people may be familiar with the former French Canadian Prime Minister named René Lévesque.
A: *

*I am a native French speaker, although not from France. 

*Lebesgue is definitely the correct spelling, and Lebesque sounds completely different; besgue sounds like beg in to beg, but the qu in que sounds like a k here.

*I don’t know what you’re reading, but I have never seen it spelled like this in my life. I assume it comes from non-French speakers who remember the spelling wrong or mix up the letters, but as I have never seen the phenomenon myself, it’s hard to tell. (Maybe if you had an article or a text where it’s written? But then again....)
Hope that helps.
A: here is what my guess on this is:
It could be from OCR or just typos during manual copy but we can't take out the fact that lowercase g in many fonts is very similar to q. Where g is like q with an extra returning arc at the bottom.
Windows fonts Arial, Century Gothic, Courier New and a bunch of other are good examples of what I mean
also Brush Script MT and some other handwriting variations have closely looking g and q.
A: It might help to note that in French (and certainly among all of the dialects of French) that certain phonemes are very easy to confuse in casual speech and certain words could be written several ways phonetically if one was uncertain of the etymology.  Thus, someone unfamiliar with the name Lebesgue (the Stutterer) could confuse it with the name Lévesque (the Bishop) and write it with a "q" rather than a "g".  It's quite common for the same French surname to have several different possible spellings, but still one usually doesn't spell one's own name incorrectly.  The transformation from "g" to "q" probably happened later by someone unfamiliar with the etymology of the name and it stuck.
Also a note on the silent "s"s: it's a carryover from Old French in which the "s"s were pronounced and then lost in Middle French with a change in vowel quality but retained in the written language.  After some more significant shifts in pronunciation and spelling reforms, many of the silent "s"s were omitted in writing (especially in between syllables) but some still remain (particularly in the last syllable of a word).  In these two names the older spelling is retained and the "s" is silent.
A: An aspect that hasn't been mentioned. The English way the cursive letter "q" is drawn is quite similar to the French "g". While there is no or little danger of confusion between "q" and "g" within the English or the French cursive alphabet, a mixed audience may actually misread "Lebesgue" from a blackboard.    
http://janbrett.com/pdf/alphabet_tracers_q_cursive.pdf 
edit In fact, to really answer the question, one should check by whom the name is misspelled. My educated guess is that whoever learned Lebesgue theory from books would almost surely write the name correctly. Unfortunately, many peolple do not go beyond class lectures or seminars, and copying from a blackboard the unknown name, "gue" is not just possibly   mistaken for "que", but very likely to be.
A: You could also think of it as a kind of play on words, although I doubt many ever intended this. So "Lebesque" would be taking a prefix coming from "Lebesgue" and applying the adjectival "que" suffix, to mean "Lebesgue-like".
A: I never saw the spelling $^{\star}$Lebesque in my life, for what it’s worth. You’re saying it’s quite common—you may well have a deeper measure-theoretic literacy than I do. At any rate, the possibility of a mistake being common does not make it correct.
The correct spelling is “Lebesgue.” As for the pronunciation, if you’re a native speaker of English, try saying $$\textit{the beg}$$ first, and then change the initial consonant “th” to “l.” This gives you the almost exact native French pronunciation. (The incorrect form $^{\star}$Lebesque would be pronounced the beck, again after substituting “l” for “th,” in French.)
A: My grandmother was a Le Besque (two words) born in 1889. I have traced my family tree back to 1675 and have seen hundreds of original documents citing the correct spelling of Le Besque, most have been archived onto my hard drive. My family originates from in and around Lorient, Bretagne. 
Noted Le Besque’s are: Jean Le Besque - Legion of Honour, Napoleonic Wars, Henri Le Besque - mathematician, Morvan Le Besque - novelist.
I have also found misspellings of Lebesque, Lebesgue and Le Besq. The misspellings were written in Parish BDM records, though I was able to link them by cross referencing.
