Functions and Analysis

    

How Likely Is It for Countably Many Almost Sure Events to Occur Simultaneously?

Authors: Yu-Lin Chou

Given a countable collection of almost sure events, the event that at least one of the events occurs is ``evidently'' almost sure. It is, however, not so trivial to assert that the event for every event of the collection to occur is almost sure. Measure theory helps to furnish a simple, definite, and affirmative answer to the question stated in the title. This useful proposition seems to rarely, if not never, occur in a teaching material regarding measure-theoretic probability; our proof in particular would help the beginning students in probability theory to get a feeling of almost sure events.

Comments: 4 Pages. expository article

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Submission history

[v1] 2020-11-06 09:03:38

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