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Theorems · Theorem · sequences and series

Equiv.summable_iff

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α}
  (e : γ ≃ β), Summable (f ∘ ⇑e) ↔ Summable f
Defined in
Mathlib.Topology.Algebra.InfiniteSum.Basic
Cited by
17 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace

Around this declaration

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

EisensteinSeries.summable_one_div_norm_rpow · cited by 4EisensteinSeries.summable…PeriodPair.summable_weierstrassPExceptSummand · cited by 3PeriodPair.summable_weier…FormalMultilinearSeries.changeOriginSeries_summable_aux₁ · cited by 3FormalMultilinearSeries.c…Summable.prod · cited by 3Summable.prodSummable.prod_symm · cited by 3Summable.prod_symmEulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum · cited by 3EulerProduct.summable_and…summable_prod_mul_pow · cited by 2summable_prod_mul_powContinuousMap.periodic_tsum_comp_add_zsmul · cited by 2ContinuousMap.periodic_ts…summable_mul_prod_iff_summable_mul_sigma_antidiagonal · cited by 2summable_mul_prod_iff_sum…summable_pnat_iff_summable_succ · cited by 2summable_pnat_iff_summabl…summable_prod_eisSummand · cited by 1summable_prod_eisSummandsummable_prod_of_nonneg · cited by 1summable_prod_of_nonnegtsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries · cited by 1tsum_eisSummand_eq_rieman…FormalMultilinearSeries.changeOrigin_eval · cited by 1FormalMultilinearSeries.c…FormalMultilinearSeries.changeOrigin_eval_of_finite · cited by 1FormalMultilinearSeries.c…DFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceAddCommMonoid · cited by 12281AddCommMonoidEquiv · cited by 8337EquivSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…Summable · cited by 778SummableEquiv.hasSum_iff · cited by 18Equiv.hasSum_iffEquiv.summable_iffCITED BYCITES

Cites7

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Cited by17

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