Theorems · Theorem · real analysis
ENNReal.ofReal_sum_of_nonneg
∀ {α : Type u_1} {s : Finset α} {f : α → ℝ},
(∀ i ∈ s, 0 ≤ f i) → ENNReal.ofReal (∑ i ∈ s, f i) = ∑ i ∈ s, ENNReal.ofReal (f i)- Defined in
- Mathlib.Data.ENNReal.BigOperators
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 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 and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement · cited by 9,879
- Finset.sumstatement and proof · cited by 5,195
- ENNReal.ofNNRealproof · cited by 1,279
- ENNReal.ofRealstatement · cited by 863
- Real.toNNRealproof · cited by 267
- Real.toNNReal_sum_of_nonnegproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- MonotoneOn.eVariationOn_eqproof · cited by 4
- ProbabilityTheory.sum_prob_mem_Ioc_leproof · cited by 1
- ProbabilityTheory.strong_law_aux1proof · cited by 1