Theorems · Theorem · functional analysis
IsEquivalent.summable_iff
Deprecated since 2026-02-07Use Asymptotics.IsEquivalent.summable_iff instead.
∀ {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)Alias of Asymptotics.IsEquivalent.summable_iff.
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- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- SummationFilter.unconditionalstatement · cited by 2,068
- FiniteDimensionalstatement · cited by 1,854
- Summablestatement · cited by 778
- Filter.cofinitestatement · cited by 251
- Asymptotics.IsEquivalentstatement · cited by 98
- Asymptotics.IsEquivalent.summable_iffproof · cited by 1
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