Theorems · Theorem · measure theory

MeasureTheory.HasFiniteIntegral.mono

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup β] [inst_1 : NormedAddCommGroup γ] {f : α → β} {g : α → γ},
  MeasureTheory.HasFiniteIntegral g μ → (∀ᵐ (a : α) ∂μ, ‖f a‖ ≤ ‖g a‖) → MeasureTheory.HasFiniteIntegral f μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral

Cited by

7 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup