Theorems · Theorem · measure theory

IntervalIntegrable.comp_mul_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_mul_left._auto_1 →
        autoParam (‖f (c * min (a / c) (b / c))‖ₑ ≠ ⊤) IntervalIntegrable.comp_mul_left._auto_3 →
          IntervalIntegrable (fun x => f (c * x)) MeasureTheory.volume (a / c) (b / c)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

6 results in Mathlib

Foundations

Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace