Theorems · Theorem · probability

ProbabilityTheory.charFunDual_map_sum_pi_eq_prod

∀ {ι : Type u_2} {E : Type u_3} [inst : MeasurableSpace E] [inst_1 : NormedAddCommGroup E] [BorelSpace E]
  [SecondCountableTopology E] [inst_4 : Fintype ι] [inst_5 : NormedSpace ℝ E] {μ : ι → MeasureTheory.Measure E}
  [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)],
  MeasureTheory.charFunDual (MeasureTheory.Measure.map (fun p => ∑ i, p i) (MeasureTheory.Measure.pi μ)) =
    ∏ i, MeasureTheory.charFunDual (μ i)

Defined in: Mathlib.Probability.Independence.CharacteristicFunction
Cited by: 1 results in Mathlib
Foundations: Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace NormedAddCommGroup BorelSpace SecondCountableTopology Fintype NormedSpace MeasureTheory.IsProbabilityMeasure

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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
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
Fintypestatement and proof · cited by 7,736
Complexstatement and proof · cited by 5,565
Finset.sumstatement · cited by 5,195
Finset.univstatement and proof · cited by 3,473
Finset.prodstatement and proof · cited by 2,356
BorelSpacestatement and proof · cited by 1,602
MeasureTheory.Measure.mapstatement · cited by 858

Cited by1

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ProbabilityTheory.charFun_map_sum_pi_eq_prodproof · cited by 0