Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.piecewise.congr_simp

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (s s_1 : Set α) (e_s : s = s_1) (hs : MeasurableSet s)
  (f f_1 : MeasureTheory.SimpleFunc α β),
  f = f_1 →
    ∀ (g g_1 : MeasureTheory.SimpleFunc α β),
      g = g_1 → MeasureTheory.SimpleFunc.piecewise s hs f g = MeasureTheory.SimpleFunc.piecewise s_1 ⋯ f_1 g_1

Defined in

Mathlib.MeasureTheory.Function.SimpleFunc

Cited by

4 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace