Theorems · Theorem · measure theory

MeasureTheory.memLp_indicator_iff_restrict

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {ε : Type u_7}
  [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddMonoid ε] {s : Set α} {f : α → ε},
  MeasurableSet s → (MeasureTheory.MemLp (s.indicator f) p μ ↔ MeasureTheory.MemLp f p (μ.restrict s))

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Indicator

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddMonoid