Theorems · Theorem · measure theory

BoundedContinuousFunction.range_toLpHom

∀ {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 : MeasureTheory.IsFiniteMeasure μ] [inst_5 : Fact (1 ≤ p)],
  (BoundedContinuousFunction.toLpHom p μ).range = MeasureTheory.Lp.boundedContinuousFunction E p μ

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

1 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEitherMeasureTheory.IsFiniteMeasureFact