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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-3/26k/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 26K / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-29

A measure-preserving transformation

T

on a probability space

(X, A, m)

is ergodic if every invariant event

A \in A

, meaning

T^{- 1} A = A

m

-null set, satisfies

m (A) \in {0, 1}

. Thus the invariant sigma-algebra is trivial modulo null sets.

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