Theorems · Theorem · functional analysis
summable_of_sum_range_norm_le
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {c : ℝ} {f : ℕ → E},
(∀ (n : ℕ), ∑ i ∈ Finset.range n, ‖f i‖ ≤ c) → Summable f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- SummationFilter.unconditionalstatement · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Finset.rangestatement and proof · cited by 1,341
- Summablestatement · cited by 778
- norm_nonnegproof · cited by 725
- summable_norm_iffproof · cited by 8
- summable_of_sum_range_leproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.