Theorems · Theorem · measure theory
ENNReal.ofReal_tsum_of_nonneg
∀ {α : Type u_1} {f : α → ℝ},
(∀ (n : α), 0 ≤ f n) → Summable f → ENNReal.ofReal (∑' (n : α), f n) = ∑' (n : α), ENNReal.ofReal (f n)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENNRealstatement · cited by 9,879
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENNReal.ofNNRealproof · cited by 1,279
- tsumstatement and proof · cited by 1,148
- ENNReal.ofRealstatement · cited by 863
- Summablestatement and proof · cited by 778
- Real.toNNRealproof · cited by 267
- ENNReal.tsum_coe_eqproof · cited by 6
- NNReal.hasSum_real_toNNReal_of_nonnegproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Egorov.measure_iUnionNotConvergentSeqproof · cited by 1
- MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNormproof · cited by 0