Product sigma algebra in the countable case

Asked Feb 02 '16 at 01:51

Active Feb 02 '16 at 01:51

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Let $(\Omega_i,\mathcal{F_i})_{i \in \mathbb{N}}$ be the countable family of measurable spaces.Then I was wondering whether the canonical product sigma algebra on the product space that is for example defined via cylinder sets agrees with

$$\sigma(\prod_{i=1}^{\infty}A_i;A_i\in \mathcal{F}_i)?$$

This seems to be somehow a natural definition to define the sigma algebra on the product space, but is it what we canonically have in mind?-This certainly works for finite products, but what is in the countable case?

asked Feb 02 '16 at 01:51

http://math.stackexchange.com/questions/1497667/product-sigma-algebra-in-countable-case-proposition-1-3-in-folland – Feb 02 '16 at 03:23
Possible duplicate of Product $\sigma$-algebra in countable case (Proposition 1.3 in Folland) – Henno Brandsma Dec 07 '18 at 22:19

Product sigma algebra in the countable case

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