Theorems · Theorem · measure theory

MeasureTheory.Lp.norm_const_le

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} (p : ENNReal) (μ : MeasureTheory.Measure α)
  [inst : NormedAddCommGroup E] [inst_1 : MeasureTheory.IsFiniteMeasure μ] (c : E),
  ‖(MeasureTheory.Lp.const p μ) c‖ ≤ ‖c‖ * μ.real Set.univ ^ (1 / p.toReal)

Defined in: Mathlib.MeasureTheory.Function.LpSpace.Indicator
Cited by: 0 results in Mathlib
Foundations: Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup MeasureTheory.IsFiniteMeasure

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Realstatement · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Norm.normstatement and proof · cited by 5,413
Set.univstatement and proof · cited by 3,945
AddSubgroupstatement · cited by 3,232
AddMonoidHomstatement · cited by 3,230
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
ENNReal.toRealstatement and proof · cited by 859

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