Semicontinuous integrands as jointly measurable maps
نویسندگان
چکیده
Suppose that (X,A) is a measurable space and Y is a metrizable, Souslin space. Let Au denote the universal completion of A. For x ∈ X, let f(x, ·) be the lower semicontinuous hull of f(x, ·). If f : X × Y → R is (Au ⊗ B(Y ),B(R))-measurable, then f is (Au ⊗ B(Y ),B(R))-measurable.
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