Theorems · Theorem · measure theory

MeasureTheory.setToFun.congr_simp

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {m : MeasurableSpace α} (μ μ_1 : MeasureTheory.Measure α)
  (e_μ : μ = μ_1) (T T_1 : Set α → E →L[ℝ] F) (e_T : T = T_1) {C C_1 : ℝ} (e_C : C = C_1)
  (hT : MeasureTheory.DominatedFinMeasAdditive μ T C) (f f_1 : α → E),
  f = f_1 → MeasureTheory.setToFun μ T hT f = MeasureTheory.setToFun μ_1 T_1 ⋯ f_1

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

10 results in Mathlib

Foundations

Depth 241 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace