Theorems · Theorem · measure theory

MeasureTheory.hasFiniteIntegral_smul_iff

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {𝕜 : Type u_7} [inst_1 : NormedRing 𝕜] [inst_2 : MulActionWithZero 𝕜 β] [IsBoundedSMul 𝕜 β] {c : 𝕜},
  IsUnit c → ∀ (f : α → β), MeasureTheory.HasFiniteIntegral (c • f) μ ↔ MeasureTheory.HasFiniteIntegral f μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral

Cited by

1 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedRingMulActionWithZeroIsBoundedSMul