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In this article, we discuss the Fine computability and the effective Fine convergence for functions on [0, 1) with respect to the Fine metric as the beginning of the effective Walsh-Fourier analysis. First we treat classically the Fine continuity and the Fine convergence. Next, we prove that Fine computability does not depend on the choice of an effective(More)
y Abstract We will speculate on the theory of the eeective sequence of unifomities on a set and its eeective limit as a methodology to vest a sequence o f r eal functions which h a ve diierent points of discontinuities with some notion of computability. Some model examples which explain the necessity of such a methodology are presented.