Theorems · Theorem · measure theory

AddCircle.measurePreserving_equivIoc

∀ (T : ℝ) [hT : Fact (0 < T)] {a : ℝ},
  MeasureTheory.MeasurePreserving (⇑(AddCircle.equivIoc T a)) MeasureTheory.volume
    (MeasureTheory.Measure.comap Subtype.val MeasureTheory.volume)

The equivalence equivIoc is measure preserving with respect to the natural volume measures.

Defined in: Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic
Cited by: 1 results in Mathlib
Foundations: Depth 248 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fact

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites32

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
Realstatement and proof · cited by 25,697
MeasureTheory.Measureproof · cited by 10,939
ENNRealproof · cited by 9,879
Equivstatement · cited by 8,337
Set.Elemstatement and proof · cited by 7,166
Set.imageproof · cited by 5,609
Set.preimageproof · cited by 4,946
MeasurableSetproof · cited by 3,075
Factstatement and proof · cited by 2,726
Set.extproof · cited by 2,266

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.MemLp.memLp_liftIocproof · cited by 1