Theorems · Theorem · measure theory

ENNReal.essSup_piecewise

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {s : Set α}
  [inst : DecidablePred fun x => x ∈ s] {g : α → ENNReal},
  MeasurableSet s → essSup (s.piecewise f g) μ = max (essSup f (μ.restrict s)) (essSup g (μ.restrict sᶜ))

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

2 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidablePred