# Help with sigma-algebra prob, pls

## Main Question or Discussion Point

Here's what it says:

"Let C be a collection of sets & E an element in the sigma-algebra generated by C. Then there is a countable subcollection C_0 contained in C such that E is an element of the sigma-algebra A_0 generated by C_0."

mathwonk
Homework Helper
i suggest recalling the definition of a sigma algebra.

i.e. for analogy, if A is a polynomial ring generated by a set S, and E is an element of A, then there is a finite subset T of S such that E belongs to the polynomial algebra generated by T.

here's my definition:
i) empty set is in C
ii) if a set is in C then so is its complement
iii) if a collection of sets is in C then so is the union of all those sets

i guess with de morgan's laws intersections of sets are also in there, but i'm not sure how that helps.

mathwonk