Theorems · Theorem · functional analysis
Summable.mul_of_nonneg
∀ {ι : Type u_2} {ι' : Type u_3} {f : ι → ℝ} {g : ι' → ℝ},
Summable f → Summable g → 0 ≤ f → 0 ≤ g → Summable fun x => f x.1 * g x.2- Defined in
- Mathlib.Analysis.Normed.Ring.InfiniteSum
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumproof · cited by 1,148
- Summablestatement and proof · cited by 778
- mul_nonnegproof · cited by 397
- Summable.mul_leftproof · cited by 47
- Summable.tsum_mul_leftproof · cited by 8
- Summable.mul_rightproof · cited by 7
- summable_prod_of_nonnegproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- Summable.mul_normproof · cited by 2
- summable_norm_sum_mul_antidiagonal_of_summable_normproof · cited by 1