Theorems · Theorem · measure theory

AntilipschitzWith.hausdorffMeasure_preimage_le

∀ {X : Type u_2} {Y : Type u_3} [inst : EMetricSpace X] [inst_1 : EMetricSpace Y] [inst_2 : MeasurableSpace X]
  [inst_3 : BorelSpace X] [inst_4 : MeasurableSpace Y] [inst_5 : BorelSpace Y] {f : X → Y} {K : NNReal} {d : ℝ},
  AntilipschitzWith K f →
    0 ≤ d →
      ∀ (s : Set Y),
        (MeasureTheory.Measure.hausdorffMeasure d) (f ⁻¹' s) ≤ ↑K ^ d * (MeasureTheory.Measure.hausdorffMeasure d) s

Defined in: Mathlib.MeasureTheory.Measure.Hausdorff
Cited by: 2 results in Mathlib
Foundations: Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: EMetricSpace EMetricSpace MeasurableSpace BorelSpace MeasurableSpace BorelSpace

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Cites61

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
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Top.topproof · cited by 9,680
Set.preimagestatement and proof · cited by 4,946
NNRealstatement and proof · cited by 4,310
LE.le.transproof · cited by 3,151
one_mulproof · cited by 2,841
Set.Nonemptyproof · cited by 2,627

Cited by2

Results whose statement or proof uses this declaration.

AntilipschitzWith.dimH_preimage_leproof · cited by 1
AntilipschitzWith.le_hausdorffMeasure_imageproof · cited by 0