Theorems · Theorem · measure theory
essSup_eq_sInf
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLinearOrder β] {m : MeasurableSpace α}
(μ : MeasureTheory.Measure α) (f : α → β), essSup f μ = sInf {a | μ {x | a < f x} = 0}- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.ofPredstatement and proof · cited by 6,101
- InfSet.sInfstatement and proof · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- essSupstatement · cited by 69
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.IsFundamentalDomain.essSup_measure_restrictproof · cited by 1
- MeasureTheory.IsAddFundamentalDomain.essSup_measure_restrictproof · cited by 1
- ProbabilityTheory.IdentDistrib.essSup_eqproof · cited by 1
- ENNReal.essSup_restrict_eq_of_support_subsetproof · cited by 1
- iSup_eq_essSupproof · cited by 0