Theorems · Theorem · measure theory

MeasureTheory.DominatedFinMeasAdditive.smul

∀ {α : Type u_1} {𝕜 : Type u_6} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_7}
  [inst : SeminormedAddCommGroup β] {T : Set α → β} {C : ℝ} [inst_1 : SeminormedAddGroup 𝕜] [inst_2 : DistribSMul 𝕜 β]
  [IsBoundedSMul 𝕜 β],
  MeasureTheory.DominatedFinMeasAdditive μ T C →
    ∀ (c : 𝕜), MeasureTheory.DominatedFinMeasAdditive μ (fun s => c • T s) (‖c‖ * C)

Defined in

Mathlib.MeasureTheory.Integral.FinMeasAdditive

Cited by

5 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupSeminormedAddGroupDistribSMulIsBoundedSMul