Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.lintegral_eq_lintegral
∀ {α : Type u_1} {m : MeasurableSpace α} (f : MeasureTheory.SimpleFunc α ENNReal) (μ : MeasureTheory.Measure α),
∫⁻ (a : α), f a ∂μ = f.lintegral μ- Cited by
- 15 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- iSup₂_leproof · cited by 96
- MeasureTheory.SimpleFunc.lintegralstatement and proof · cited by 55
- le_iSup₂_of_leproof · cited by 52
- MeasureTheory.lintegral_defproof · cited by 15
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_constproof · cited by 123
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasurableEmbedding.lintegral_mapproof · cited by 10
- MeasureTheory.lintegral_eq_iSup_eapprox_lintegralproof · cited by 7
- MeasureTheory.iSup_lintegral_measurable_le_eq_lintegralproof · cited by 4
- MeasureTheory.L1.SimpleFunc.norm_eq_sum_mulproof · cited by 2
- MeasureTheory.exists_setLIntegral_compl_ltproof · cited by 1
- MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memLpproof · cited by 1
- MeasureTheory.lintegral_add_auxproof · cited by 1
- MeasureTheory.exists_upperSemicontinuous_le_lintegral_leproof · cited by 1
- MeasureTheory.SimpleFunc.integral_eq_lintegral'proof · cited by 1
- MeasureTheory.exists_lt_lintegral_simpleFunc_of_lt_lintegralproof · cited by 1