Theorems · Theorem · real analysis
AntitoneOn.integral_le_sum_Ico
∀ {a b : ℕ} {f : ℝ → ℝ}, a ≤ b → AntitoneOn f (Set.Icc ↑a ↑b) → ∫ (x : ℝ) in ↑a..↑b, f x ≤ ∑ x ∈ Finset.Ico a b, f ↑x- Defined in
- Mathlib.Analysis.SumIntegralComparisons
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finsetproof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Set.Iccstatement and proof · cited by 1,702
- Finset.rangeproof · cited by 1,341
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Nat.cast_addproof · cited by 586
- intervalIntegralstatement and proof · cited by 546
- Finset.Icostatement and proof · cited by 450
- AntitoneOnstatement and proof · cited by 266
Cited by3
Results whose statement or proof uses this declaration.
- AntitoneOn.integral_le_tsum_comp_addproof · cited by 1
- log_add_one_le_harmonicproof · cited by 1
- MonotoneOn.sum_le_integral_Icoproof · cited by 0