Theorems · Theorem · measure theory

MeasureTheory.continuous_integral_integral

∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
  [inst_4 : NormedSpace ℝ E] [MeasureTheory.SFinite μ], Continuous fun f => ∫ (x : α), ∫ (y : β), ↑↑f (x, y) ∂ν ∂μ

The map that sends an L¹-function f : α × β → E to ∫∫f is continuous.

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

1 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteNormedSpaceMeasureTheory.SFinite