Theorems · Theorem · probability

ContinuousLinearMap.integral_id_map

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace ℝ E] [inst_5 : NormedSpace 𝕜 F]
  [inst_6 : NormedSpace ℝ F] [CompleteSpace E] [CompleteSpace F] [inst_9 : MeasurableSpace E]
  {μ : MeasureTheory.Measure E} [OpensMeasurableSpace E] [inst_11 : MeasurableSpace F] [BorelSpace F]
  [SecondCountableTopology F],
  MeasureTheory.Integrable id μ →
    ∀ (L : E →L[𝕜] F), ∫ (x : F), x ∂MeasureTheory.Measure.map (⇑L) μ = L (∫ (x : E), x ∂μ)

Defined in

Mathlib.Probability.Moments.Basic

Cited by

2 results in Mathlib

Foundations

Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpaceNormedSpaceCompleteSpaceCompleteSpaceMeasurableSpaceOpensMeasurableSpaceMeasurableSpaceBorelSpaceSecondCountableTopology