Die Arbeit beantwortet eine von M. Steinhaus (Studia 1 (1929), 81) aufgeworfene Frage dahingehend, daß im metrischen Raum \(E\) aller stetigen Funktionen von der Periode l diejenigen, deren beide rechtsseitige Ableitungen in mindestens einem Punkte endlich sind, eine Menge erster Kategorie bilden. Der Beweis stützt sich auf trigonometrische Polynome. (IV 3 A.)

It is proved that the class of continuous functions without finite one-sided derivative in any point is the complementary set to a set of \( 1^{\text {st }} \) category of Baire in the space of continuous functions. This gives the affirmative answer to a problem of Steinhaus who proved an analogous result but by some general theorems of the functional calculus and only for the continuous functions without finite one-sided derivative almost everywhere (Studia Math. 1, 81). There follows from the theorem of Mazurkiewicz a new proof of the existence of continuous functions without finite one-sided derivative in any point. This method cannot however be applied to prove the existence of continuous functions of Besicovitch’s type i. e. without finite or infinite onesided derivative everywhere.