Theorems · Theorem · measure theory

MeasureTheory.charFun_map_smul

∀ {E : Type u_2} {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E} [inst : SeminormedAddCommGroup E]
  [inst_1 : InnerProductSpace ℝ E] [BorelSpace E] (r : ℝ) (t : E),
  MeasureTheory.charFun (MeasureTheory.Measure.map (fun x => r • x) μ) t = MeasureTheory.charFun μ (r • t)

Defined in: Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedAddCommGroup InnerProductSpace BorelSpace

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Cites27

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

Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Complexstatement and proof · cited by 5,565
InnerProductSpacestatement and proof · cited by 3,523
SeminormedAddCommGroupstatement and proof · cited by 2,671
MeasureTheory.integralproof · cited by 1,779
Complex.ofRealproof · cited by 1,654
BorelSpacestatement and proof · cited by 1,602
Inner.innerproof · cited by 1,089
Complex.Iproof · cited by 866
MeasureTheory.Measure.mapstatement and proof · cited by 858

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.charFun_map_smul_compproof · cited by 1
MeasureTheory.charFun_map_mulproof · cited by 0