Theorems · Theorem · measure theory

MeasureTheory.charFunDual_conv

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {mE : MeasurableSpace E} [BorelSpace E]
  [SecondCountableTopology E] {μ ν : MeasureTheory.Measure E} [MeasureTheory.IsFiniteMeasure μ]
  [MeasureTheory.IsFiniteMeasure ν] (L : StrongDual ℝ E),
  MeasureTheory.charFunDual (μ.conv ν) L = MeasureTheory.charFunDual μ L * MeasureTheory.charFunDual ν L

The characteristic function of a convolution of measures is the product of the respective characteristic functions.

Defined in: Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace BorelSpace SecondCountableTopology MeasureTheory.IsFiniteMeasure MeasureTheory.IsFiniteMeasure

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Cites38

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

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
Complexstatement and proof · cited by 5,565
Filter.Eventuallyproof · cited by 3,134
MeasureTheory.aeproof · cited by 2,352
MeasureTheory.integralproof · cited by 1,779
Complex.ofRealproof · cited by 1,654
BorelSpacestatement and proof · cited by 1,602

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mulproof · cited by 3