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In my first course in probability theory, our textbook was Kai Lai Chung's Elementary Probability Theory. Chung, starting from the tenth page* and continuing throughout the book, uses the notation $AB$ for $A\cap B$; the professor for the course also used this notation, and did so without comment. However, earlier today I made use of this notation while talking to a different professor, and she had never heard of it. A quick internet search following our conversation turned up no examples of Chung's notation. Thus, my question:

How common is it to denote the intersection $A\cap B$ by $AB$?


*I have the fourth edition.

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  • $\begingroup$ In some of my undergraduate and graduate courses, my professors used $A\cdot B$ for $A\cap B$ and $A+B$ for $A\cup B$. I am in my 70's so perhaps you would have to search very old papers to find this notation. $\endgroup$ – John Wayland Bales May 16 '17 at 19:43
  • $\begingroup$ I still see it in the context of probability, even here. You'll see people write things like $Pr(AB)=Pr(A)Pr(B\mid A)$. I don't know that I've encountered the equivalent notation for union however. $\endgroup$ – JMoravitz May 16 '17 at 19:47
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    $\begingroup$ I've never seen it, but it might be more common in probability theory than in other mathematics. One reason for this is the formulas $P(A \cap B) = P(A) P(B)$ and $P(A \cup B) = P(A) + P(B)$. These would then be written with the same operator for both the sets/events and the probabilities. $\endgroup$ – md2perpe May 16 '17 at 19:56
  • $\begingroup$ Not so uncommon a century ago; see Felix Hausdorff, Set theory, (Engl.transl.of the 3rd German ed., 1937), page 18. $\endgroup$ – Mauro ALLEGRANZA May 16 '17 at 20:20
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    $\begingroup$ The "formulas" that @md2perpe refers to should have the disclaimer that the first is true if and only if $A$ and $B$ are independent events and the second is true if $A$ and $B$ are mutually exclusive (and only if $A\cap B$ is an almost impossible or an impossible event). $\endgroup$ – JMoravitz May 16 '17 at 20:58

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