Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.withDensity_apply

∀ {X : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedAddCommGroup G]
  [inst_5 : NormedSpace ℝ G] {μ : MeasureTheory.VectorMeasure X F} {f : X → E} {B : E →L[ℝ] F →L[ℝ] G} {s : Set X},
  μ.Integrable f → (μ.withDensity f B) s = ∫ᵛ (x : X) in s, f x ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.WithDensityVec

Cited by

7 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace