Theorems · Theorem · complex analysis
ValueDistribution.proximity_congr_codiscrete
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {f g : ℂ → E} {a : WithTop E} {r : ℝ},
f =ᶠ[Filter.codiscrete ℂ] g → r ≠ 0 → ValueDistribution.proximity f a r = ValueDistribution.proximity g a rIf two functions differ only on a discrete set, then their proximity functions agree, except perhaps at radius 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
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Cites12
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- WithTopstatement and proof · cited by 3,754
- Filter.EventuallyEqstatement and proof · cited by 1,912
- absproof · cited by 1,814
- Metric.sphereproof · cited by 371
- Filter.EventuallyEq.filter_monoproof · cited by 59
- Filter.codiscretestatement and proof · cited by 34
- ValueDistribution.proximitystatement · cited by 28
- Filter.codiscreteWithin_monoproof · cited by 9
- ValueDistribution.proximity_congr_codiscreteWithinproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_congr_codiscreteproof · cited by 0