Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_mono_enorm_ae

∀ {α : Type u_1} {ε : Type u_2} {ε' : Type u_3} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : ENorm ε] [inst_1 : ENorm ε'] {f : α → ε} {g : α → ε'},
  (∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ ‖g x‖ₑ) → MeasureTheory.eLpNorm f p μ ≤ MeasureTheory.eLpNorm g p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

7 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENormENorm