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Theorems · Theorem · abstract harmonic analysis

MeasureTheory.Measure.dirac_conv

∀ {M : Type u_1} [inst : AddMonoid M] [inst_1 : MeasurableSpace M] [MeasurableAdd₂ M] (x : M)
  (μ : MeasureTheory.Measure M) [MeasureTheory.SFinite μ],
  (MeasureTheory.Measure.dirac x).conv μ = MeasureTheory.Measure.map (fun y => x + y) μ
Defined in
Mathlib.MeasureTheory.Group.Convolution
Cited by
1 results in Mathlib
Foundations
Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidMeasurableSpaceMeasurableAdd₂MeasureTheory.SFinite
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Around this declaration

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

MeasureTheory.Measure.dirac_zero_conv · cited by 0Measure.dirac_zero_convMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureAddMonoid · cited by 2864AddMonoidMeasureTheory.Measure.map · cited by 858Measure.mapMeasureTheory.SFinite · cited by 449MeasureTheory.SFiniteMeasureTheory.Measure.dirac · cited by 210Measure.diracmeasurable_const · cited by 156measurable_constMeasurableAdd₂ · cited by 155MeasurableAdd₂measurable_id' · cited by 145measurable_id'Measurable.prodMk · cited by 115Measurable.prodMkMeasureTheory.Measure.map_map · cited by 67Measure.map_mapMeasurable.fst · cited by 51Measurable.fstMeasurable.snd · cited by 51Measurable.sndMeasureTheory.Measure.conv · cited by 41Measure.convMeasurable.fun_add · cited by 11Measurable.fun_addMeasure.dirac_convCITED BYCITES

Cites16

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Cited by1

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