Theorems · Theorem · measure theory
ENNReal.hasSum_coe
∀ {α : Type u_1} {f : α → NNReal} {r : NNReal}, HasSum (fun a => ↑(f a)) ↑r ↔ HasSum f r- Cited by
- 6 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- ENNRealstatement · cited by 9,879
- nhdsproof · cited by 5,554
- Finset.sumproof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- Filter.Tendstoproof · cited by 3,814
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- HasSumstatement · cited by 518
- SummationFilter.filterproof · cited by 110
Cited by6
Results whose statement or proof uses this declaration.
- ENNReal.tsum_coe_ne_top_iff_summableproof · cited by 11
- ENNReal.tsum_coe_eqproof · cited by 6
- NNReal.hasSum_iff_tendsto_natproof · cited by 2
- HasSum.isProbabilityMeasure_sum_dirac_nnrealproof · cited by 1
- NNReal.exists_le_hasSum_of_leproof · cited by 1
- ENNReal.hasSum_ltproof · cited by 1