Theorems · Theorem · functional analysis
Asymptotics.IsEquivalent.summable_iff
∀ {ι : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
{f g : ι → E}, Asymptotics.IsEquivalent Filter.cofinite f g → (Summable f ↔ Summable g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 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
- SummationFilter.unconditionalstatement · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Summablestatement · cited by 778
- Filter.cofinitestatement and proof · cited by 251
- Asymptotics.IsEquivalentstatement and proof · cited by 98
- Asymptotics.IsEquivalent.isThetaproof · cited by 9
- Asymptotics.IsTheta.summable_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsEquivalent.summable_iffproof · cited by 0