Is Schilling's Corollary 8.9 really a corollary?

Corollary 8.9 is not a corollary of Theorem 8.8, but it does seem to be a corollary of Lemma 8.1, which gives NASC for measurability of a function $u:X\mapsto R$. One sufficient condition for measurability of $u$ is that $\{u>a\}\in {\cal A}$ for every $a\in R$; this condition is applied in the proof of Corollary 8.9.

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Measure Theory

Proof Verification

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