map_mono_of_aemeasurable — Mathlib

English

Same as previous: if μ ≤ ν and f is AEM with respect to ν, then μ.map f ≤ ν.map f.

Русский

То же самое: если μ ≤ ν и f AЕ-мeасируемо относительно ν, тогда μ.map f ≤ ν.map f.

LaTeX

$$$\text{(same as above)}$$$

Lean4

theorem map_mono_of_aemeasurable {f : α → δ} (h : μ ≤ ν) (hf : AEMeasurable f ν) : μ.map f ≤ ν.map f :=
  le_iff.2 fun s hs ↦ by simpa [hf, hs, hf.mono_measure h] using h (f ⁻¹' s)

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