identDistrib_mk — Mathlib

English

For IdentDistrib f g μ ν and a measurable set s, μ(f⁻¹(s)) = ν(g⁻¹(s)).

Русский

Для IdentDistrib f g μ ν и измеримого множества s верно μ(f⁻¹(s)) = ν(g⁻¹(s)).

LaTeX

$$$\text{measure_mem_eq }(h)\ {s:\ Set γ}\ (hs: MeasurableSet s) : μ (f^{-1}(s)) = ν (g^{-1}(s))$$$

Lean4

theorem _root_.MeasureTheory.AEMeasurable.identDistrib_mk (hf : AEMeasurable f μ) : IdentDistrib f (hf.mk f) μ μ :=
  IdentDistrib.of_ae_eq hf hf.ae_eq_mk

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