Theorems · Theorem · measure theory

MeasureTheory.Measure.le_map_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {f : α → β}, AEMeasurable f μ → ∀ (s : Set β), μ (f ⁻¹' s) ≤ (MeasureTheory.Measure.map f μ) s

Even if s is not measurable, we can bound map f μ s from below. See also MeasurableEquiv.map_apply.

Defined in

Mathlib.MeasureTheory.Measure.Map

Cited by

5 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound