Theorems · Theorem · measure theory

MeasureTheory.indicatorConstLp_disjoint_union

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ⊤)
  (hμt : μ t ≠ ⊤),
  Disjoint s t →
    ∀ (c : E),
      MeasureTheory.indicatorConstLp p ⋯ ⋯ c =
        MeasureTheory.indicatorConstLp p hs hμs c + MeasureTheory.indicatorConstLp p ht hμt c

The indicator of a disjoint union of two sets is the sum of the indicators of the sets.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Indicator

Cited by

1 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup