Theorems · Theorem · measure theory

MeasureTheory.ae_measure_preimage_mul_right_lt_top

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [MeasurableMul₂ G] {s : Set G} [MeasurableInv G]
  (μ' ν' : MeasureTheory.Measure G) [MeasureTheory.SigmaFinite μ'] [MeasureTheory.SigmaFinite ν']
  [μ'.IsMulLeftInvariant] [ν'.IsMulLeftInvariant], μ' s ≠ ⊤ → ∀ᵐ (x : G) ∂μ', ν' ((fun x_1 => x_1 * x) ⁻¹' s) < ⊤

Defined in: Mathlib.MeasureTheory.Group.Prod
Cited by: 1 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace Group MeasurableMul₂ MeasurableInv MeasureTheory.SigmaFinite MeasureTheory.SigmaFinite MeasureTheory.Measure.IsMulLeftInvariant MeasureTheory.Measure.IsMulLeftInvariant

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites47

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
Top.topstatement and proof · cited by 9,680
Groupstatement and proof · cited by 6,238
Set.imageproof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
mul_oneproof · cited by 3,885
Filter.Eventuallystatement · cited by 3,134
MeasurableSetproof · cited by 3,075

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zeroproof · cited by 1