Theorems · Theorem · measure theory
essSup_congr_ae
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
[inst : ConditionallyCompleteLattice β] {f g : α → β}, f =ᵐ[μ] g → essSup f μ = essSup g μ- Defined in
- Mathlib.MeasureTheory.Function.EssSup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- ConditionallyCompleteLatticestatement and proof · cited by 364
- essSupstatement · cited by 69
- Filter.limsup_congrproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- essSup_map_measureproof · cited by 3
- MeasureTheory.Lp.eLpNorm_exponent_top_lim_eq_essSup_liminfproof · cited by 1
- essInf_congr_aeproof · cited by 0
- MeasureTheory.eLpNormEssSup_congr_aeproof · cited by 0