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L p ‐Computability
Author(s) -
Zhong Ning,
Zhang BingYu
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450403
Subject(s) - computability , computable function , mathematics , function (biology) , combinatorics , discrete mathematics , computable analysis , evolutionary biology , biology
In this paper we investigate conditions for L p ‐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 ⊂ ℝ q , we show that an L p function f ∈ L p ( I ) is L P ‐computable if and only if (i) f is sequentially computable as a linear functional and (ii) the L p ‐modulus function of f is effectively continuous at the origin of ℝ q .