Theorems · Theorem · measure theory

MeasureTheory.integrable_const_iff_enorm

∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] {c : ε},
  ‖c‖ₑ ≠ ⊤ → (MeasureTheory.Integrable (fun x => c) μ ↔ ‖c‖ₑ = 0 ∨ MeasureTheory.IsFiniteMeasure μ)

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

5 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENorm