Preiss, David; Zajíček, Luděk On Dini and approximate Dini derivates of typical continuous functions. (English) Zbl 1009.26010 Real Anal. Exch. 26(2000-2001), No. 1, 401-412 (2001). Summary: In the thirties, Banach, Mazurkiewicz and Jarník found relations connecting Dini derivates of a typical continuous function on \([0, 1]\) at all points of \((0, 1)\). We prove, answering a question of K. M. Garg, that there are no further relations of this sort. An analogous result is proved also for approximate Dini derivates. The aim of this note is to present relatively simple proofs of these results. An article containing an improvement of these results in several directions (with a considerably more complicated proof) is in preparation. Cited in 2 Documents MSC: 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems Keywords:approximate Dini derivates PDFBibTeX XMLCite \textit{D. Preiss} and \textit{L. Zajíček}, Real Anal. Exch. 26, No. 1, 401--412 (2001; Zbl 1009.26010)