Theorems · Theorem · functional analysis

MeasureTheory.MemLp.of_le_enorm

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {ε : Type u_7} {ε' : Type u_8}
  [inst : TopologicalSpace ε] [inst_1 : TopologicalSpace ε'] [inst_2 : ContinuousENorm ε] [inst_3 : ContinuousENorm ε']
  {f : α → ε} {g : α → ε'},
  MeasureTheory.MemLp g p μ →
    MeasureTheory.AEStronglyMeasurable f μ → (∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ ‖g x‖ₑ) → MeasureTheory.MemLp f p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceContinuousENormContinuousENorm