Theorems · Theorem · real analysis
Real.toNNReal_sum_of_nonneg
∀ {ι : Type u_2} {s : Finset ι} {f : ι → ℝ}, (∀ i ∈ s, 0 ≤ f i) → (∑ a ∈ s, f a).toNNReal = ∑ a ∈ s, (f a).toNNReal- Defined in
- Mathlib.Data.NNReal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 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.
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement · cited by 4,310
- Finset.sum_congrproof · cited by 2,323
- NNReal.toRealproof · cited by 1,260
- Real.toNNRealstatement and proof · cited by 267
- Finset.sum_nonnegproof · cited by 91
- NNReal.coe_injproof · cited by 30
- Real.coe_toNNRealproof · cited by 27
- NNReal.coe_sumproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.ofReal_sum_of_nonnegproof · cited by 4