# What does the symbol $\leqq$ mean?

What does the symbol $$\leqq$$ mean?

I am reading a paper on by Lehman on dependence, and here I find

$$\ldots$$we compare the probability of any quadrant $$X \leqq x$$, $$Y \leqq y$$ under the distribution $$F$$ of $$(X,Y)$$ with the corresponding probability in the case of independence”.

Is $$\leqq$$ the same as $$\leq$$?

• @January I have no idea why this question acquired downvotes. It seems perfectly clear and potentially interesting. I haven't seen the notation before myself. I have upvoted. – Peter Woolfitt Mar 31 '17 at 8:57
• "Is ≦ the same as ≤?" Yes. – Did Mar 31 '17 at 8:58
• Thanks! Given that I have only basic mathematical education, I am always anxious that I miss some specific definition or meaning. The proofs are hard enough for me without this. – January Mar 31 '17 at 9:02
• This is not a stupid question at all. Some symbols are so bizarre ! en.wikipedia.org/wiki/List_of_mathematical_symbols is a good place to visit. – Claude Leibovici Mar 31 '17 at 9:08
• Great link! How did I miss it. Big thanks! – January Mar 31 '17 at 9:21

I would say that it is a symbol of less or equal "without contracting," which is the same as putting $\leq$

it's not exactly the same by what i read on wiki, there it writes

"x ≧ y means that each component of vector x is greater than or equal to each corresponding component of vector y."

so my guess is that it would not be appropriate to use regular ≤ when talking about vectors/lists, ≤ is usually used to compare single things eg size of array but not elements of array.

you might say that if A={1,2,6,42} B={1,2,4,8} A≦B

but if A={0,2,6,42} A is NOT ≦B because A1 is NOT ≤B1

This is just my interpretation no one confirmed it, and there is some nonsense in wiki.

• It is worth noting that the Wikipedia "list of notation" breaks things down by context. It specifically notes that in vector analysis, $\leqq$ and $\geqq$ can be understood elementwise. However, just above that entry, it notes that $\leqq$ and $\geqq$ are often used as synonyms of $\le$ and $\ge$ – Xander Henderson Sep 10 '19 at 15:05