Let F be a sigma-algebra of subsets of Ω, and let B Î F: Show that G = {A Ç B : A Î F} is a sigma-algebra of subsets of B.

Lt. Definition ist eine sigma-algebra wie folgt beschrieben:
A collection of subsets of S (Sample Space) is called sigma algebra, denoted by , if it satiesfies the following three properties:
1. The empty set is an element of the sigma-algebra.
2. If A is an element of the sigma-algebra, then A^c is also an element (closed under complementation).
3. If A₁, A₂, … is an element of the sigma-algebra, then the union of all A_i is also an element (closed under countable unions).

Ich verstehe leider nicht so ganz, wie ich das zeigen soll? Bzw. was diese Definition konkret bedeutet?

Kann mir vl. jemand helfen?

Danke euch!!