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

If a measure $P$ can take value of $+\infty $, does countable additivity ($\sigma$-additivity) imply continuity at $\emptyset$? If not, what is a good example?

share|cite|improve this question
Not set-theory. Plus, $P$ is not a probability, so the tag should be measure-theory instead.) – Andrés E. Caicedo Jan 23 '13 at 22:56
The reals with Lebesgue measure form a counterexample, right? Take $A_n=(n,\infty)$. Their intersection is empty. – Andrés E. Caicedo Jan 23 '13 at 22:57

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.