Theorems · Theorem · measure theory

IntervalIntegrable.comp_add_right_iff

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {f : ℝ → ε} {a b : ℝ}
  [TopologicalSpace.PseudoMetrizableSpace ε] {c : ℝ},
  autoParam (‖f (min a b + c)‖ₑ ≠ ⊤) IntervalIntegrable.comp_add_right_iff._auto_1 →
    (IntervalIntegrable (fun x => f (x + c)) MeasureTheory.volume a b ↔
      IntervalIntegrable f MeasureTheory.volume (a + c) (b + c))

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

3 results in Mathlib

Foundations

Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace