Talk:Equivalence of Definitions of Sigma-Algebra

Definition 2 is wrong?

 * Explain why. --prime mover (talk) 05:09, 30 May 2022 (UTC)

Counterexample
Let $X=\set {1,2,3,4}$ and $\Sigma = \set {\emptyset, X, \set {1,2}, \set{3,4}, \set {1,3}, \set {2,4}}$.

$\struct {X,\Sigma}$ satisfies Definition 2 but not Definition 1.


 * I believe the origin of this is misquotation. The source of the definition defines condition 2 to be $A \setminus B$ instead of $\map {\complement_X} A = X \setminus A$. I'm not sure of the ramifications of this adjustment so I'll leave my interference at that. &mdash; Lord_Farin (talk) 12:50, 30 May 2022 (UTC)


 * I see some of this stuff was posted up by me when I first tried to take on Avner Friedman but lost interest on page 3. I don't know where the unsourced presentation of the definition of sigma algebra comes from, haven't a clue where I got it from, but it's not from Friedman. Might have been off the web. I will take a look later and see what sense I can make of it. I may end up removing unsourced material if I cannot resolve its soundness. --prime mover (talk) 16:34, 30 May 2022 (UTC)


 * There is a second definition in Friedman as Theorem 1.1.1 which roughly corresponds to def 2. &mdash; Lord_Farin (talk) 17:11, 30 May 2022 (UTC)