Theorems · Theorem · functional analysis
Summable.of_norm
∀ {ι : Type u_1} {E : Type u_3} [inst : SeminormedAddCommGroup E] [CompleteSpace E] {f : ι → E},
(Summable fun a => ‖f a‖) → Summable f- Cited by
- 40 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- le_rflproof · cited by 1,558
- Summablestatement and proof · cited by 778
- Summable.of_norm_boundedproof · cited by 25
Cited by40
Results whose statement or proof uses this declaration.
- tendstoUniformlyOn_tsumproof · cited by 9
- summable_norm_iffproof · cited by 8
- tendstoUniformlyOn_tsum_of_cofinite_eventuallyproof · cited by 6
- summable_mul_of_summable_normproof · cited by 5
- EulerProduct.eulerProduct_hasProdproof · cited by 4
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- LSeriesSummable_of_le_const_mul_rpowproof · cited by 3
- NormedSpace.expSeries_summable'proof · cited by 3
- MeasureTheory.setToFun_tsumproof · cited by 3
- two_mul_riemannZeta_eq_tsum_int_inv_pow_of_evenproof · cited by 2
- DirichletCharacter.LSeriesSummable_mulproof · cited by 2
- EulerProduct.one_sub_inv_eq_geometric_of_summable_normproof · cited by 2