Measure, Integration & Real Analysis · Problem 12.3

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · independent-events-equivalences

Problem

Suppose

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

is a probability space and

A, B \in \mathcal{F}

. Prove that the following are equivalent. •

A

and

B

are independent events. •

A

and

\Omega \setminus B

are independent events. •

\Omega \setminus A

and

B

are independent events. •

\Omega \setminus A

and

\Omega \setminus B

are independent events.