Theorems · Theorem · measure theory

MeasureTheory.Measure.comap_apply_le

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

Defined in: Mathlib.MeasureTheory.Measure.Comap
Cited by: 1 results in Mathlib
Foundations: Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Set.imagestatement and proof · cited by 5,609
MeasurableSetproof · cited by 3,075
le_reflproof · cited by 2,061
MeasureTheory.NullMeasurableSetstatement and proof · cited by 337
MeasureTheory.Measure.comapstatement and proof · cited by 96
MeasureTheory.Measure.comap_apply₀proof · cited by 6
MeasureTheory.Measure.comap_undefproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.FiniteMeasure.mass_comap_leproof · cited by 1