Theorems · Theorem · real analysis
StieltjesFunction.ae_hasDerivAt
∀ (f : StieltjesFunction ℝ), ∀ᵐ (x : ℝ), HasDerivAt (↑f) (f.measure.rnDeriv MeasureTheory.volume x).toReal x
A Stieltjes function is almost everywhere differentiable, with derivative equal to the Radon-Nikodym derivative of the associated Stieltjes measure with respect to Lebesgue.
- Defined in
- Mathlib.Analysis.Calculus.Monotone
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites86
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by1
Results whose statement or proof uses this declaration.
- Monotone.ae_hasDerivAtproof · cited by 1