Theorems · Theorem · probability

ProbabilityTheory.charFun_map_add_prod_eq_mul

∀ {E : Type u_2} {mE : MeasurableSpace E} [inst : NormedAddCommGroup E] [BorelSpace E] [SecondCountableTopology E]
  [inst_3 : InnerProductSpace ℝ E] {μ ν : MeasureTheory.Measure E} [MeasureTheory.IsProbabilityMeasure μ]
  [MeasureTheory.IsProbabilityMeasure ν],
  MeasureTheory.charFun (MeasureTheory.Measure.map (fun p => p.1 + p.2) (μ.prod ν)) =
    MeasureTheory.charFun μ * MeasureTheory.charFun ν

Defined in: Mathlib.Probability.Independence.CharacteristicFunction
Cited by: 0 results in Mathlib
Foundations: Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup BorelSpace SecondCountableTopology InnerProductSpace MeasureTheory.IsProbabilityMeasure MeasureTheory.IsProbabilityMeasure

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Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
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
BorelSpacestatement and proof · cited by 1,602
MeasureTheory.Measure.mapstatement and proof · cited by 858
SecondCountableTopologystatement and proof · cited by 750
MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
MeasureTheory.Measure.prodstatement and proof · cited by 353
measurable_idproof · cited by 89

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