Theorems · Theorem · measure theory

ContinuousMap.toLp_norm_le

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} (μ : MeasureTheory.Measure α)
  [inst : TopologicalSpace α] [inst_1 : BorelSpace α] [inst_2 : NormedAddCommGroup E]
  [inst_3 : SecondCountableTopologyEither α E] [inst_4 : CompactSpace α] [inst_5 : MeasureTheory.IsFiniteMeasure μ]
  [inst_6 : Fact (1 ≤ p)] {𝕜 : Type u_4} [inst_7 : NontriviallyNormedField 𝕜] [inst_8 : NormedSpace 𝕜 E],
  ‖ContinuousMap.toLp p μ 𝕜‖ ≤ ↑(MeasureTheory.measureUnivNNReal μ) ^ p.toReal⁻¹

Bound for the operator norm of ContinuousMap.toLp.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

0 results in Mathlib

Foundations

Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEitherCompactSpaceMeasureTheory.IsFiniteMeasureFactNontriviallyNormedFieldNormedSpace