Mathlib Map

Theorems · Theorem · sequences and series

summable_of_hasFiniteSupport

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α}
  {L : SummationFilter β} [L.HasSupport], Function.HasFiniteSupport f → Summable f L
Defined in
Mathlib.Topology.Algebra.InfiniteSum.Basic
Cited by
12 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpaceSummationFilter.HasSupport

Around this declaration

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

tsum_eq_finsum · cited by 4tsum_eq_finsumSummable.of_finite · cited by 4Summable.of_finitePeriodPair.weierstrassPExcept_add · cited by 3PeriodPair.weierstrassPEx…PeriodPair.coeff_weierstrassPExceptSeries · cited by 3PeriodPair.coeff_weierstr…MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_weightedOrder_atTop_nhds_top · cited by 2WithPiTopology.summable_p…Nat.infinite_setOfPred_prime_and_eq_mod · cited by 2Nat.infinite_setOfPred_pr…MvPowerSeries.WithPiTopology.summable_of_tendsto_weightedOrder_atTop_nhds_top · cited by 1WithPiTopology.summable_o…PeriodPair.derivWeierstrassPExcept_sub · cited by 1PeriodPair.derivWeierstra…PowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top · cited by 1WithPiTopology.summable_o…PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top · cited by 1WithPiTopology.summable_p…FormalMultilinearSeries.changeOrigin_eval_of_finite · cited by 1FormalMultilinearSeries.c…summable_of_finite_support · cited by 0summable_of_finite_supportTopologicalSpace · cited by 24529TopologicalSpaceAddCommMonoid · cited by 12281AddCommMonoidSummable · cited by 778SummableSummationFilter · cited by 607SummationFilterFunction.HasFiniteSupport · cited by 113Function.HasFiniteSupportSet.Finite.mem_toFinset · cited by 74Finite.mem_toFinsetFunction.mem_support · cited by 54Function.mem_supportSummationFilter.HasSupport · cited by 38SummationFilter.HasSupportsummable_of_ne_finset_zero · cited by 4summable_of_ne_finset_zerosummable_of_hasFiniteSupportCITED BYCITES

Cites9

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

Cited by12

Results whose statement or proof uses this declaration.