le_toMeasure_apply — Mathlib

English

The outer measure toMeasure composed with toOuterMeasure recovers the original measure: μ.toOuterMeasure.toMeasure ≤ μ.

Русский

Внешняя мера toMeasure, затем каратейодори, восстанавливают исходную меру: μ.toOuterMeasure.toMeasure = μ.

LaTeX

$$$$ μ.toOuterMeasure.toMeasure(\leq) = μ $$$$

Lean4

theorem le_toMeasure_apply (m : OuterMeasure α) (h : ms ≤ m.caratheodory) (s : Set α) : m s ≤ m.toMeasure h s :=
  m.le_trim s

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