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category:Math/Real Calculus and Topology date:2025-06 logpath:NumAnalysis.Lebesgue keyword:sigma-algebra keyword:monotone class theorem keyword:Dynkin pi-lambda theorem keyword:measure theory keyword:Lebesgue measure keyword:simple function keyword:adapted sequence keyword:Beppo Levi (monotone convergence) theorem keyword:Fatou lemma keyword:Lebesgue (dominated convergence) theorem keyword:Lebesgue induction principle keyword:Tonelli theorem keyword:Bochner integral