Theorems · Theorem · real analysis
MonotoneOn.sum_le_integral_Ico
∀ {a b : ℕ} {f : ℝ → ℝ}, a ≤ b → MonotoneOn f (Set.Icc ↑a ↑b) → ∑ x ∈ Finset.Ico a b, f ↑x ≤ ∫ (x : ℝ) in ↑a..↑b, f x- Defined in
- Mathlib.Analysis.SumIntegralComparisons
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finset.sumstatement and proof · cited by 5,195
- Set.Iccstatement and proof · cited by 1,702
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- intervalIntegralstatement and proof · cited by 546
- Finset.Icostatement and proof · cited by 450
- MonotoneOnstatement and proof · cited by 311
- Finset.sum_neg_distribproof · cited by 65
- neg_le_neg_iffproof · cited by 57
- intervalIntegral.integral_negproof · cited by 21
- MonotoneOn.negproof · cited by 8
- AntitoneOn.integral_le_sum_Icoproof · cited by 3
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