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Theorems · Theorem · sequences and series

Summable.subtype

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommGroup α] [IsUniformAddGroup α] {f : β → α}
  [CompleteSpace α], Summable f → ∀ (p : β → Prop), Summable (f ∘ Subtype.val)
Defined in
Mathlib.Topology.Algebra.InfiniteSum.Group
Cited by
15 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceAddCommGroupIsUniformAddGroupCompleteSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

tendstoUniformlyOn_tsum · cited by 9tendstoUniformlyOn_tsumtendstoUniformlyOn_tsum_of_cofinite_eventually · cited by 6tendstoUniformlyOn_tsum_o…tendsto_tsum_of_dominated_convergence · cited by 2tendsto_tsum_of_dominated…Summable.tsum_subtype_add_tsum_subtype_compl · cited by 2Summable.tsum_subtype_add…Summable.tsum_subtype_le · cited by 2Summable.tsum_subtype_leEulerProduct.exp_tsum_primes_log_eq_tsum · cited by 1EulerProduct.exp_tsum_pri…tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries · cited by 1tsum_eisSummand_eq_rieman…contDiff_tsum_of_eventually · cited by 1contDiff_tsum_of_eventual…summable_subtype_and_compl · cited by 1summable_subtype_and_complEisensteinSeries.eisensteinSeries_tendstoLocallyUniformly · cited by 1EisensteinSeries.eisenste…EisensteinSeries.norm_le_tsum_norm · cited by 1EisensteinSeries.norm_le_…HasSum.tsum_fiberwise · cited by 1HasSum.tsum_fiberwiseNat.Primes.summable_rpow · cited by 1Primes.summable_rpowtsum_eq_tsum_primes_of_support_subset_prime_powers · cited by 1tsum_eq_tsum_primes_of_su…tsum_eq_tsum_primes_add_tsum_primes_of_support_subset_prime_powers · cited by 0tsum_eq_tsum_primes_add_t…AddCommGroup · cited by 12871AddCommGroupCompleteSpace · cited by 2532CompleteSpaceSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…UniformSpace · cited by 2040UniformSpaceSummable · cited by 778SummableIsUniformAddGroup · cited by 342IsUniformAddGroupSubtype.coe_injective · cited by 205Subtype.coe_injectiveSummable.comp_injective · cited by 22Summable.comp_injectiveSummable.subtypeCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

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