Theorems · Theorem · complex analysis
circleIntegrable_congr_codiscreteWithin
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {c : ℂ} {R : ℝ} {f₁ f₂ : ℂ → E},
f₁ =ᶠ[Filter.codiscreteWithin (Metric.sphere c |R|)] f₂ → (CircleIntegrable f₁ c R ↔ CircleIntegrable f₂ c R)Circle integrability is invariant when functions change along discrete sets.
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- Foundations
- Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- Filter.EventuallyEqstatement and proof · cited by 1,912
- absstatement and proof · cited by 1,814
- Filter.EventuallyEq.symmproof · cited by 408
- Metric.spherestatement and proof · cited by 371
- Filter.codiscreteWithinstatement and proof · cited by 87
- CircleIntegrablestatement and proof · cited by 86
- CircleIntegrable.congr_codiscreteWithinproof · cited by 3
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