Notation of joint event probability I have been using several books and I came across different notations that I am assuming they mean the same thing, but I am not 100% sure.
Are these probabilities the same thing?
$P(AB) \equiv P(A,B) \equiv P(A \land B) \equiv P(A \cap B) \equiv P(A \times B)$?
Edited:
added $P(A \times B)$
 A: *

*$P(A, B)$ is a pretty standard notation for joint probability two events $A$, $B$, both being true,

*$P(A \cap B)$ means the same, but it is using set theory notation for intersection, in probability theory it is just as a notation used for saying $A$ and $B$,

*$P(A \land B)$ is the same, but is using a notation borrowed from logic for conjunction,

*$P(AB)$ or $P(A \times B)$ is a confusing choice of notation; as noticed in the comment if you multiply binary numbers then $AB = A \land B$, so it would be equivalent.  
However, if we start talking about random variables, then the notation $p(x, y) = P(X = x, Y = y)$ still has the same sense, while $p(xy)$ is not the same thing, since this is a distribution of a product of two random variables, that is not the same as their joint distribution (both formally, since $p(xy)$ is a function of single variable, while $p(x,y)$ is a function of two variables, and in terms of the probabilities returned by it). To give an example, say that you ask what is $P(X=5, Y=3)$, since $5\times 3 = 15$, then $XY = 15$ would be true both if $x=3$ and $y=5$, and if $x=5$ and $y=3$. This would be the case, informally speaking, if there was some kind of equivalence between $X$ and $Y$, and they were independent of each other. 
A: $P(AB)$ is not a standard notation, $AB$ can be the name of the event, or as in your example, each letter can denote different events. But, $P(A,B)$, which maybe used for shorthand purposes, and others most probably mean the same thing. 
