Theorems · Theorem · measure theory
ENNReal.essSup_const_mul
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {a : ENNReal},
essSup (fun x => a * f x) μ = a * essSup f 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- essSupstatement · cited by 69
- ENNReal.limsup_const_mulproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul'proof · cited by 3
- MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mulproof · cited by 2
- MeasureTheory.eLpNormEssSup_const_smulproof · cited by 0
- StrongDual.norm_toLpₗ_leproof · cited by 0