Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.const_mul_lintegral
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (f : MeasureTheory.SimpleFunc α ENNReal)
(x : ENNReal), (MeasureTheory.SimpleFunc.const α x * f).lintegral μ = x * f.lintegral μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Set.preimageproof · cited by 4,946
- Finset.sum_congrproof · cited by 2,323
- mul_assocproof · cited by 1,667
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- Finset.mul_sumproof · cited by 196
- MeasureTheory.SimpleFunc.rangeproof · cited by 97
- MeasureTheory.SimpleFunc.lintegralstatement · cited by 55
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasureTheory.lintegral_iSupproof · cited by 16
- MeasureTheory.lintegral_const_mul_leproof · cited by 2