Measure, Integration & Real Analysis · Problem 5A.2

Product Measures — Sheldon Axler

Mathematics — Measure Theory · product-sigma-algebra-diagonal

Problem

Suppose (X,S)(X, \mathcal{S}) is a measurable space. Prove that if E∈S⊗SE \in \mathcal{S} \otimes \mathcal{S}, then {x∈X:(x,x)∈E}∈S.\{x \in X : (x, x) \in E\} \in \mathcal{S}.

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