Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $(S_i,\mathbf{S}_i)$ be a sequence of Borel spaces, i.e. such that for all $i$ there is a 1-1 bimeasurable map $\varphi_i:S_i\to T_i$, where $T_i$ is a Borel subset of [0,1].

Is $\prod_{i=1}^n S_i$, equipped with the product $\sigma$-algebra, a Borel space?

What about $\prod_{i=1}^\infty S_i$, with the $\sigma$-algebra $\mathbf{A}$, where $\mathbf{A}$ is the smallest $\sigma$-algebra containing elements of the form $\prod T_i$, where $T_i$=$S_i$ for all but finitely many $i$'s?

Thank you.

share|cite|improve this question
Hint: $[0,1]^n$ and $[0,1]^\infty$ are Borel spaces. – Nate Eldredge Jul 9 '11 at 18:44

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.