Theorems · Theorem · probability
ProbabilityTheory.hasSum_integral_poissonMeasure
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {r : NNReal} {f : ℕ → E},
MeasureTheory.Integrable f (ProbabilityTheory.poissonMeasure r) →
HasSum (fun n => (Real.exp (-↑r) * ↑r ^ n / ↑n.factorial) • f n)
(∫ (n : ℕ), f n ∂ProbabilityTheory.poissonMeasure r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- NNReal.toRealstatement and proof · cited by 1,260
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_poissonMeasure'proof · cited by 1