Theorems · Theorem · complex analysis
ValueDistribution.characteristic_eventually_nonneg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} {a : WithTop E},
0 ≤ᶠ[Filter.atTop] ValueDistribution.characteristic f aThe characteristic function is asymptotically non-negative.
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- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- WithTopstatement and proof · cited by 3,754
- Filter.atTopstatement · cited by 2,405
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Filter.EventuallyLEstatement · cited by 383
- Filter.eventually_ge_atTopproof · cited by 111
- ValueDistribution.characteristicstatement · cited by 26
- ValueDistribution.characteristic_nonnegproof · cited by 1
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