Theorems · Theorem · functional analysis

MeasureTheory.MemLp.mono_exponent

∀ {α : Type u_1} {ε : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ε}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {p q : ENNReal} [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.MemLp f q μ → p ≤ q → MeasureTheory.MemLp f p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp

Cited by

11 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormMeasureTheory.IsFiniteMeasure