Theorems · Theorem · real analysis
MonotoneOn.intervalIntegral_slope_le
∀ {f : ℝ → ℝ} {a b c : ℝ},
MonotoneOn f (Set.Icc a (b + c)) → a ≤ b → 0 ≤ c → ∫ (x : ℝ) in a..b, slope f x (x + c) ≤ f (b + c) - f aIf f is monotone on a..(b + c) where a ≤ b and 0 ≤ c, then the interval integral of
fun x ↦ slope f x (x + c) on a..b is at most f (b + c) - f a.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Nat.cast_zeroproof · cited by 1,870
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Cited by1
Results whose statement or proof uses this declaration.
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2