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Theorems · Theorem · real analysis

AbsolutelyContinuousOnInterval.fun_add

∀ {F : Type u_2} [inst : SeminormedAddCommGroup F] {a b : ℝ} {f g : ℝ → F},
  AbsolutelyContinuousOnInterval f a b →
    AbsolutelyContinuousOnInterval g a b → AbsolutelyContinuousOnInterval (fun i => f i + g i) a b

Eta-expanded form of AbsolutelyContinuousOnInterval.add

Defined in
Mathlib.MeasureTheory.Function.AbsolutelyContinuous
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Foundations
Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroup
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Real · cited by 25697RealSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupAbsolutelyContinuousOnInterval · cited by 31AbsolutelyContinuousOnInt…AbsolutelyContinuousOnInterval.add · cited by 2AbsolutelyContinuousOnInt…AbsolutelyContinuousOnInterva…CITED BYCITES

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