Theorems · Theorem · measure theory

BoundedContinuousFunction.norm_integral_le_mul_norm

∀ {X : Type u_1} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] (μ : MeasureTheory.Measure X) {E : Type u_2}
  [inst_2 : NormedAddCommGroup E] [OpensMeasurableSpace X] [SecondCountableTopology E] [inst_5 : MeasurableSpace E]
  [BorelSpace E] [inst_7 : NormedSpace ℝ E] [MeasureTheory.IsFiniteMeasure μ] (f : BoundedContinuousFunction X E),
  ‖∫ (x : X), f x ∂μ‖ ≤ μ.real Set.univ * ‖f‖

Defined in

Mathlib.MeasureTheory.Integral.BoundedContinuousFunction

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceSecondCountableTopologyMeasurableSpaceBorelSpaceNormedSpaceMeasureTheory.IsFiniteMeasure