Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_mono_ae

∀ {α : Type u_1} {F : Type u_5} {G : Type u_6} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup F] [inst_1 : NormedAddCommGroup G] {f : α → F} {g : α → G},
  (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖) → MeasureTheory.eLpNorm f p μ ≤ MeasureTheory.eLpNorm g p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

6 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup