Theorems · Theorem · real analysis
AbsolutelyMonotoneOn.of_contDiff
∀ {f : ℝ → ℝ} {s : Set ℝ}, ContDiff ℝ (↑⊤) f → (∀ (n : ℕ), ∀ x ∈ s, 0 ≤ iteratedDeriv n f x) → AbsolutelyMonotoneOn f sA globally C^∞ function whose iterated derivatives are nonnegative on s is absolutely
monotone on s. The set s need not satisfy UniqueDiffOn.
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- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- WithTop.somestatement and proof · cited by 1,128
- ContDiffstatement and proof · cited by 352
- iteratedDerivstatement and proof · cited by 188
- ftaylorSeriesproof · cited by 11
- AbsolutelyMonotoneOnstatement · cited by 6
- iteratedDeriv_eq_iteratedFDerivproof · cited by 4
- HasFTaylorSeriesUpTo.hasFTaylorSeriesUpToOnproof · cited by 2
- ContDiff.ftaylorSeriesproof · cited by 1
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