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Theorems · Theorem · real analysis

AbsolutelyContinuousOnInterval.mul

∀ {a b : ℝ} {f g : ℝ → ℝ},
  AbsolutelyContinuousOnInterval f a b →
    AbsolutelyContinuousOnInterval g a b → AbsolutelyContinuousOnInterval (f * g) a b

If f and g are absolutely continuous on uIcc a b, then f * g is absolutely continuous on uIcc a b.

Defined in
Mathlib.MeasureTheory.Function.AbsolutelyContinuous
Cited by
1 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AbsolutelyContinuousOnInterval.fun_mul · cited by 1AbsolutelyContinuousOnInt…Real · cited by 25697RealAbsolutelyContinuousOnInterval · cited by 31AbsolutelyContinuousOnInt…AbsolutelyContinuousOnInterval.smul · cited by 2AbsolutelyContinuousOnInt…AbsolutelyContinuousOnInterva…CITED BYCITES

Cites3

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Cited by1

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