Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.lintegral_mono_fun
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : MeasureTheory.SimpleFunc α ENNReal},
f ≤ g → f.lintegral μ ≤ g.lintegral μ- Cited by
- 2 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.
Cites16
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
- Set.preimageproof · cited by 4,946
- le_reflproof · cited by 2,061
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- mul_le_mul'proof · cited by 274
- le_sup_leftproof · cited by 265
- Finset.sum_le_sumproof · cited by 182
- MeasureTheory.SimpleFunc.rangeproof · cited by 97
- MeasureTheory.SimpleFunc.lintegralstatement and proof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.lintegral_monoproof · cited by 6
- MeasureTheory.SimpleFunc.le_sup_lintegralproof · cited by 0