Theorems · Theorem · real analysis
NNReal.coe_sum
∀ {ι : Type u_2} (s : Finset ι) (f : ι → NNReal), ↑(∑ i ∈ s, f i) = ∑ i ∈ s, ↑(f i)- Defined in
- Mathlib.Data.NNReal.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- map_sumproof · cited by 455
- NNReal.toRealHomproof · cited by 13
Cited by24
Results whose statement or proof uses this declaration.
- ENNReal.toReal_sumproof · cited by 15
- EuclideanSpace.norm_eqproof · cited by 8
- PiLp.nnnorm_eq_of_L2proof · cited by 5
- nnnorm_sum_leproof · cited by 4
- Matrix.frobenius_norm_defproof · cited by 2
- PiLp.norm_sq_eq_of_L2proof · cited by 2
- PiLp.nnnorm_eq_sumproof · cited by 2
- Real.Lr_rpow_le_Lp_mul_Lqproof · cited by 2
- nnnorm_sum_le_of_leproof · cited by 1
- Real.toNNReal_sum_of_nonnegproof · cited by 1
- MeasureTheory.SignedMeasure.exists_subset_lt_enorm_apply_of_lt_variationproof · cited by 1
- Real.rpow_sum_le_const_mul_sum_rpowproof · cited by 1