Theorems · Theorem · measure theory

AddCircle.integral_preimage

∀ (T : ℝ) [hT : Fact (0 < T)] {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (t : ℝ)
  (f : AddCircle T → E), ∫ (a : ℝ) in Set.Ioc t (t + T), f ↑a = ∫ (b : AddCircle T), f b

The integral of an almost-everywhere strongly measurable function over AddCircle T is equal to the integral over an interval $(t, t + T]$ in ℝ of its lift to ℝ.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic

Cited by

2 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactNormedAddCommGroupNormedSpace