Theorems · Theorem · functional analysis
Metric.exists_subseq_summable_dist_of_cauchySeq
∀ {α : Type u_1} [inst : PseudoMetricSpace α] (u : ℕ → α),
CauchySeq u → ∃ f, StrictMono f ∧ Summable fun i => dist (u (f (i + 1))) (u (f i))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement · cited by 2,068
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- le_of_ltproof · cited by 1,175
- Summablestatement · cited by 778
- StrictMonostatement and proof · cited by 706
- div_posproof · cited by 337
- pow_posproof · cited by 292
- CauchySeqstatement and proof · cited by 131
- dist_nonnegproof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- NormedAddCommGroup.completeSpace_of_summable_imp_tendstoproof · cited by 1