Theorems · Theorem · measure theory

MeasureTheory.dist_indicatorConstLp_eq_norm

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

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Indicator

Cited by

2 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup