mono_measure — Mathlib

English

The composition of a continuous function g with an AEStronglyMeasurable f is AEStronglyMeasurable.

Русский

Состав непрерывной функции g с AEStronglyMeasurable f сохраняет AE‑строгое измерение.

LaTeX

$$$\\text{Continuous}(g) \\Rightarrow AEStronglyMeasurable f μ \\Rightarrow AEStronglyMeasurable (\\lambda x. g(f(x))) μ$$$

Lean4

theorem mono_measure {ν : Measure α} (hf : AEStronglyMeasurable[m] f μ) (h : ν ≤ μ) : AEStronglyMeasurable[m] f ν :=
  ⟨hf.mk f, hf.stronglyMeasurable_mk, Eventually.filter_mono (ae_mono h) hf.ae_eq_mk⟩

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