Measure, Integration & Real Analysis · Problem 12.2

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · independent-events-example

Problem

Suppose

P

is Lebesgue measure on

[0,1]

. Give an example of two disjoint Borel subsets

A

and

B

[0,1]

such that

P(A) = P(B) = \frac{1}{2}

[0, \frac{1}{2}]

and

A

are independent, and

[0, \frac{1}{2}]

and

B

are independent.