Theorems · Theorem · measure theory
ENNReal.essSup_eq_zero_iff
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal}, essSup f μ = 0 ↔ f =ᵐ[μ] 0- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- essSupstatement · cited by 69
- ENNReal.limsup_eq_zero_iffproof · cited by 1
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