Theorems · Theorem · measure theory
iSup_eq_essSup
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : CompleteLinearOrder β]
{f : α → β}, (∀ ⦃x : α⦄ ⦃a : β⦄, a < f x → μ {y | a < f y} ≠ 0) → ⨆ x, f x = essSup f μ- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLinearOrder
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Cites15
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- 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
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- not_ltproof · cited by 306
- iSup_leproof · cited by 190
- CompleteLinearOrderstatement and proof · cited by 126
- essSupstatement · cited by 69
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