Theorems · Definition · measure theory

MeasureTheory.Lp.boundedContinuousFunction

{α : Type u_1} →
  (E : Type u_2) →
    {m0 : MeasurableSpace α} →
      (p : ENNReal) →
        (μ : MeasureTheory.Measure α) →
          [inst : TopologicalSpace α] →
            [BorelSpace α] →
              [inst_2 : NormedAddCommGroup E] →
                [SecondCountableTopologyEither α E] → AddSubgroup ↥(MeasureTheory.Lp E p μ)

An additive subgroup of Lp E p μ, consisting of the equivalence classes which contain a bounded continuous representative.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

7 results in Mathlib

Foundations

Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEither