Theorems · Theorem · measure theory
MeasureTheory.lintegral_sum_measure
∀ {α : Type u_1} {m : MeasurableSpace α} {ι : Type u_4} (f : α → ENNReal) (μ : ι → MeasureTheory.Measure α),
∫⁻ (a : α), f a ∂MeasureTheory.Measure.sum μ = ∑' (i : ι), ∫⁻ (a : α), f a ∂μ i- Cited by
- 16 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Finset.sumproof · cited by 5,195
- iSupproof · cited by 2,415
- SummationFilter.unconditionalstatement · cited by 2,068
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- tsumstatement · cited by 1,148
- CompleteLatticeproof · cited by 1,048
- MeasureTheory.SimpleFuncproof · cited by 411
Cited by16
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_countable'proof · cited by 4
- MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_acproof · cited by 3
- MeasureTheory.Measure.prod_sum_leftproof · cited by 3
- MeasureTheory.lintegral_countproof · cited by 3
- MeasureTheory.withDensity_sumproof · cited by 3
- MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_acproof · cited by 3
- ProbabilityTheory.Kernel.comp_sum_rightproof · cited by 2
- MeasureTheory.integrable_sum_measureproof · cited by 2
- MeasureTheory.lintegral_iUnion_leproof · cited by 2
- MeasureTheory.lintegral_iUnion₀proof · cited by 2
- MeasureTheory.Integrable.summable_integralproof · cited by 2
- MeasureTheory.hasSum_lintegral_measureproof · cited by 1