Theorems · Theorem · measure theory
ENNReal.coe_tsum
∀ {α : Type u_1} {f : α → NNReal}, Summable f → ↑(tsum f) = ∑' (a : α), ↑(f a)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 155 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.
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- tsumstatement and proof · cited by 1,148
- Summablestatement and proof · cited by 778
- HasSumproof · cited by 518
- HasSum.tsum_eqproof · cited by 150
- ENNReal.tsum_coe_eqproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- ENNReal.tsum_coe_ne_top_iff_summableproof · cited by 11
- NNReal.summable_sigmaproof · cited by 7
- MeasureTheory.setToFun_tsumproof · cited by 3
- NNReal.tsum_eq_toNNReal_tsumproof · cited by 3
- ENNReal.tendsto_tsum_compl_atTop_zeroproof · cited by 2
- MeasureTheory.ProbabilityMeasure.apply_iUnion_leproof · cited by 0
- MeasureTheory.FiniteMeasure.apply_iUnion_leproof · cited by 0