This short paper concerns “peso nullo” subsets of the real line defined in 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 sigma-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.
Null sets with respect to a continuous function / Aversa, VINCENZO LIBERO; DE SIMONE, Anna. - In: TATRA MOUNTAINS MATHEMATICAL PUBLICATIONS. - ISSN 1210-3195. - 52:(2012), pp. 47-51. [10.2478/v10127-012-0024-x]
Null sets with respect to a continuous function
AVERSA, VINCENZO LIBERO;DE SIMONE, ANNA
2012
Abstract
This short paper concerns “peso nullo” subsets of the real line defined in 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 sigma-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.