Abstract
Let C be the space of all real-valued continuous functions defined on the unit interval provided with the uniform norm. In the Scottish Book, Banach raised the question of the descriptive class of the subset D of C consisting of all functions which are differentiable at each point of [0,1]. Banach pointed out that D forms a coanalytic subset of C and asked whether D is a Borel set. Later Mazurkiewicz showed that D is not a Borel set [3]. In this paper, we shall investigate the subset M of C consisting of all functions which do not have a finite derivative at any point of [0,1]. It is well known that M is residual in C [2]. We shall prove the following theorem.
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