Measure, Integration & Real Analysis · Problem 12.1

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · independent-events-complement

Problem

Suppose

(\Omega, \mathcal{F}, P)

is a probability space and

A \in \mathcal{F}

. Prove that

A

and

\Omega \setminus A

are independent if and only if

P(A) = 0

P(A) = 1