Dense Sets in Spaces of Integrable Functions
نویسندگان
چکیده
منابع مشابه
Complexity theory for spaces of integrable functions
This paper investigates second-order representations in the sense of Kawamura and Cook for spaces of integrable functions that regularly show up in analysis. It builds upon prior work about the space of continuous functions on the unit interval: Kawamura and Cook introduced a representation inducing the right complexity classes and proved that it is the weakest second-order representation such ...
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Let A be a set of integers and let h ≥ 2. For every integer n, let rA,h(n) denote the number of representations of n in the form n = a1 + · · ·+ah, where ai ∈ A for 1 ≤ i ≤ h, and a1 ≤ · · · ≤ ah. The function rA,h : Z→ N, where N = N∪{0,∞}, is the representation function of order h for A. We prove that every function f : Z → N satisfying lim inf|n|→∞ f(n) ≥ g is the representation function of ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1157