Theorems · Theorem · measure theory

fst_integral

∀ {X : Type u_1} {E : Type u_3} {F : Type u_4} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F]
  [CompleteSpace F] {f : X → E × F}, MeasureTheory.Integrable f μ → (∫ (x : X), f x ∂μ).1 = ∫ (x : X), (f x).1 ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap

Cited by

3 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceCompleteSpace