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

I want to formally define a uniform probability measure on $\{0,1\}^\omega$ (infinite binary sequences). Is it possible? What is the exact definition? I see it should have the property "the set of sequences with exactly $k$ fixed values has probability $\frac{1}{2^k}$", but it's not a definition...

share|cite|improve this question
Kolmogorov's theorems provide a formal construction. But by identifying $\{0,1\}^{\omega}$ with $[0, 1]$ using binary representation as usual, we immediately obtain a uniform measure inheritted from the Lebesgue measure. – Sangchul Lee Apr 29 '12 at 9:31

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.