Theorems · Theorem · measure theory
MeasureTheory.setLAverage_le_essSup
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s : Set α) (f : α → ENNReal),
⨍⁻ (x : α) in s, f x ∂μ ≤ essSup f μ- Defined in
- Mathlib.MeasureTheory.Integral.Average
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Set.univproof · cited by 3,945
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.IsFiniteMeasureproof · cited by 1,078
- zero_smulproof · cited by 716
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.laverage_le_essSupproof · cited by 0