Theorems · Theorem · measure theory

IntervalIntegrable.comp_add_left

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

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace