Theorems · Theorem · probability
ProbabilityTheory.charFun_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 : InnerProductSpace ℝ E] (μ : ι → MeasureTheory.Measure E)
[∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)],
MeasureTheory.charFun (MeasureTheory.Measure.map (fun p => ∑ i, p i) (MeasureTheory.Measure.pi μ)) =
∏ i, MeasureTheory.charFun (μ i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Fintypestatement and proof · cited by 7,736
- Complexstatement · cited by 5,565
- Finset.sumstatement · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- BorelSpacestatement and proof · cited by 1,602
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