Theorems · Theorem · measure theory

IntervalIntegrable.trans_iff

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {f : ℝ → ε} {a b c : ℝ}
  {μ : MeasureTheory.Measure ℝ} [TopologicalSpace.PseudoMetrizableSpace ε],
  b ∈ Set.uIcc a c → (IntervalIntegrable f μ a c ↔ IntervalIntegrable f μ a b ∧ IntervalIntegrable f μ b c)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

0 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace