Theorems · Theorem · complex analysis
ValueDistribution.log_counting_zero_sub_logCounting_top
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : ProperSpace 𝕜] {E : Type u_2}
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {f : 𝕜 → E},
Function.locallyFinsuppWithin.logCounting (MeromorphicOn.divisor f Set.univ) =
ValueDistribution.logCounting f 0 - ValueDistribution.logCounting f ⊤The logarithmic counting function associated with the divisor of f is the difference between
logCounting f 0 and logCounting f ⊤.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univstatement and proof · cited by 3,945
- WithTopstatement · cited by 3,754
- AddMonoidHomstatement · cited by 3,230
- map_subproof · cited by 565
- ProperSpacestatement and proof · cited by 190
- Function.locallyFinsuppWithinproof · cited by 127
Cited by1
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_sub_characteristic_invproof · cited by 2