Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrable.integrableOn_nhds_isCompact

∀ {X : Type u_1} {ε : Type u_3} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace ε]
  [inst_3 : ContinuousENorm ε] {f : X → ε} {μ : MeasureTheory.Measure X} [TopologicalSpace.PseudoMetrizableSpace ε],
  MeasureTheory.LocallyIntegrable f μ →
    ∀ {k : Set X}, IsCompact k → ∃ u, IsOpen u ∧ k ⊆ u ∧ MeasureTheory.IntegrableOn f u μ

If a function is locally integrable, then it is integrable on an open neighborhood of any compact set.

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

1 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpaceContinuousENormTopologicalSpace.PseudoMetrizableSpace