Talk:Lévy's Inversion Formula

Why not write $\map \Pr {a < X < b}$

Under the assumption $\map \Pr {X \in \set {a, b} } = 0$, of course:

$\map \Pr {a < X \le b} = \map \Pr {a < X < b} = \map \Pr {a \le X \le b} = \map \Pr {a \le X < b}$

Among them, usually, $\map \Pr {a < X \le b}$ is the preferable choice in probability theory.

One reason is related to Definition:Cumulative Distribution Function, i.e. the fact:

$\map {F_X} b - \map {F_X} a = \map \Pr {a < X \le b}$

--Usagiop (talk) 19:18, 22 April 2023 (UTC)

Can the above information be captured, in a page explaining why $\map \Pr {a < X \le b}$ is the preferred choice, and linking to it via a link on the theorem statement? --prime mover (talk) 19:21, 22 April 2023 (UTC)

I improved the statement to include the information, too. Now, it should look more natural. --Usagiop (talk) 20:49, 22 April 2023 (UTC)

Good stuff. This is collaboration at its finest. --prime mover (talk) 21:13, 22 April 2023 (UTC)