Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.iSup_eapprox_apply
∀ {α : Type u_1} [inst : MeasurableSpace α] {f : α → ENNReal},
Measurable f → ∀ (a : α), ⨆ n, (MeasureTheory.SimpleFunc.eapprox f n) a = f a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- ENNRealstatement and proof · cited by 9,879
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- Measurablestatement and proof · cited by 1,499
- ENNReal.ofNNRealproof · cited by 1,279
- le_of_ltproof · cited by 1,175
- lt_of_le_of_ltproof · cited by 432
- le_of_not_gtproof · cited by 430
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasureTheory.lintegral_eq_iSup_eapprox_lintegralproof · cited by 7
- Measurable.ennreal_inductionproof · cited by 7
- Measurable.lintegral_kernel_prod_rightproof · cited by 5
- MeasureTheory.SimpleFunc.iSup_coe_eapproxproof · cited by 1
- MeasureTheory.lintegral_add_auxproof · cited by 1
- MeasureTheory.SimpleFunc.tsum_eapproxDiffproof · cited by 1
- ProbabilityTheory.Kernel.lintegral_compProd'proof · cited by 1