Theorems · Theorem · measure theory

IntervalIntegrable.mono_fun_enorm

∀ {ε : Type u_3} {ε' : Type u_4} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε]
  [inst_2 : TopologicalSpace ε'] [inst_3 : ENormedAddMonoid ε'] {f : ℝ → ε} {a b : ℝ} {μ : MeasureTheory.Measure ℝ}
  [TopologicalSpace.PseudoMetrizableSpace ε] [TopologicalSpace.PseudoMetrizableSpace ε'] {g : ℝ → ε'},
  IntervalIntegrable f μ a b →
    MeasureTheory.AEStronglyMeasurable g (μ.restrict (Set.uIoc a b)) →
      ((fun x => ‖g x‖ₑ) ≤ᵐ[μ.restrict (Set.uIoc a b)] fun x => ‖f x‖ₑ) → IntervalIntegrable g μ a b

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

TopologicalSpaceENormedAddMonoidTopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpaceTopologicalSpace.PseudoMetrizableSpace