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

What's an atomic probability space? Can a complete probability space be an atomic probability space?

share|cite|improve this question
up vote 3 down vote accepted

An atom of a probability space is a measurable set $A$ with positive measure $P(A)$ and the property that for each measurable subset $B\subseteq A$, either $P(B)=0$ or $P(B)=P(A)$. The probability space is purely atomic if every measurable set with positive measure contains an atom. If $A$ is an atom, it will still be an atom in the completion of the probability space. So yes, a complete probability space can be atomic. Every countable probability space is purely atomic.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.