Theorems · Theorem · measure theory

MeasureTheory.integrableOn_singleton

∀ {α : Type u_1} {ε' : Type u_4} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε']
  [inst_1 : ESeminormedAddMonoid ε'] {f : α → ε'} {x : α} [MeasurableSingletonClass α],
  autoParam (‖f x‖ₑ ≠ ⊤) MeasureTheory.integrableOn_singleton._auto_1 →
    autoParam (μ {x} < ⊤) MeasureTheory.integrableOn_singleton._auto_3 → MeasureTheory.IntegrableOn f {x} μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

7 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddMonoidMeasurableSingletonClass