Theorems · Theorem · sequences and series
summable_of_sum_le
∀ {ι : Type u_3} {f : ι → ℝ} {c : ℝ}, 0 ≤ f → (∀ (u : Finset ι), ∑ x ∈ u, f x ≤ c) → Summable f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- Set.rangeproof · cited by 4,705
- iSupproof · cited by 2,415
- SummationFilter.unconditionalstatement · cited by 2,068
- Summablestatement · cited by 778
- tendsto_atTop_ciSupproof · cited by 13
- Finset.sum_mono_set_of_nonnegproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- ZLattice.summable_norm_rpowproof · cited by 4
- summable_finsetProd_of_summable_nonnegproof · cited by 3
- AbsolutelyContinuousOnInterval.const_of_ae_hasDerivAt_zeroproof · cited by 1
- Real.tsum_le_of_sum_leproof · cited by 1