Theorems · Theorem · measure theory

BoundedContinuousFunction.isBounded_range_integral

∀ {X : Type u_1} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] {E : Type u_2} [inst_2 : NormedAddCommGroup E]
  [OpensMeasurableSpace X] [SecondCountableTopology E] [inst_5 : MeasurableSpace E] [BorelSpace E]
  [inst_7 : NormedSpace ℝ E] {ι : Type u_3} (μs : ι → MeasureTheory.Measure X)
  [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μs i)] (f : BoundedContinuousFunction X E),
  Bornology.IsBounded (Set.range fun i => ∫ (x : X), f x ∂μs i)

Defined in

Mathlib.MeasureTheory.Integral.BoundedContinuousFunction

Cited by

2 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceSecondCountableTopologyMeasurableSpaceBorelSpaceNormedSpaceMeasureTheory.IsProbabilityMeasure