Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_restrict_eq_of_support_subset

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {ε : Type u_7}
  [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {s : Set α} {f : α → ε},
  Function.support f ⊆ s → MeasureTheory.eLpNorm f p (μ.restrict s) = MeasureTheory.eLpNorm f p μ

For a function f with support in s, the Lᵖ norms of f with respect to μ and μ.restrict s are the same.

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

1 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoid