Null sets with respect to a continuous function

Rok, strany: 2012, 47 - 51

This short paper concerns \lq\lq peso nullo'' subsets of the real line defined in [Caccioppoli, R.: \textit{L'integrazione e la ricerca delle primitive rispetto ad una funzione continua qualunque}, Ann. Mat. Pura Appl. \textbf{40} (1955),\mbox{15–34}]. The framework is that of integration with respect to a function $g$ which is continuous but not necessarily of bounded variation. Here we shall call these sets $g$-null. Since the family of $g$-null sets is a $σ$-ideal, the natural question is whether it is a family of null sets with respect to a Borel measure on the real line. The paper gives a negative answer to this question.

ISO 690:

Aversa, V., De Simone, A. 2012. Null sets with respect to a continuous function. In Tatra Mountains Mathematical Publications, vol. 52, no.2, pp. 47-51. 1210-3195.

APA:

Aversa, V., De Simone, A. (2012). Null sets with respect to a continuous function. Tatra Mountains Mathematical Publications, 52(2), 47-51. 1210-3195.