Theorems · Theorem · functional analysis
Asymptotics.IsEquivalent.summable_iff_nat
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {f g : ℕ → E},
Asymptotics.IsEquivalent Filter.atTop f g → (Summable f ↔ Summable g)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Filter.atTopstatement and proof · cited by 2,405
- SummationFilter.unconditionalstatement · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Summablestatement · cited by 778
- Asymptotics.IsEquivalentstatement and proof · cited by 98
- Asymptotics.IsEquivalent.isThetaproof · cited by 9
- Asymptotics.IsTheta.summable_iff_natproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.summable_one_div_nat_add_rpowproof · cited by 0
- IsEquivalent.summable_iff_natproof · cited by 0