Lp‐Computability
Ning Zhong, Bing‐Yu Zhang · Mathematical logic quarterly · 1999
Abstract In this paper we investigate conditions for Lp‐computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ⊂ ℝq, we show that an Lp function f ∈ Lp(I) is LP‐computable if and only if (i) f is sequentially computable as a linear functional and (ii) the Lp‐modulus function of f is effectively continuous at the origin of ℝq.