Theorems · Theorem · real analysis
Real.posLog_sum
∀ {α : Type u_1} (s : Finset α) (f : α → ℝ), (∑ t ∈ s, f t).posLog ≤ Real.log ↑s.card + ∑ t ∈ s, (f t).posLogEstimate for log⁺ of a sum. See Real.posLog_add for a variant involving
just two summands.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- add_zeroproof · cited by 2,707
- Finset.cardstatement and proof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- le_reflproof · cited by 2,061
- absproof · cited by 1,814
- Set.Iciproof · cited by 1,070
- Real.logstatement and proof · cited by 939
- add_le_addproof · cited by 666
- nsmul_eq_mulproof · cited by 369
Cited by2
Results whose statement or proof uses this declaration.
- Real.posLog_addproof · cited by 1
- Real.posLog_norm_sum_leproof · cited by 1