# Product Sigma Algebra Problem

1. Nov 20, 2013

### haljordan45

1. The problem statement, all variables and given/known data

Given 3 measure spaces (X,A,$\mu$), (Y,B,$\zeta$), (Z,C,$\gamma$), show that the product of the three sigma algebras A, B, and C is associative, meaning that:

AxBxC=(AxB)xC=Ax(BxC)

2. Relevant equations

We can make use of the fact that XxYxZ=(XxY)xZ=Xx(YxZ)

3. The attempt at a solution

I've tried looking at showing the generating set for AxBxC lies in the other two sigma algebras but am having trouble drawing the direct connection. Any help would be greatly appreciated.