Null sets with respect to a continuous function
Aversa, Vincenzo ; De Simone, Anna
Tatra Mountains Mathematical Publications, Tome 51 (2012), / Harvested from Mathematical Institute
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This short paper concerns  \lq\lq peso nullo'' subsets of thereal line defined by Renato Caccioppoli \cite{ca}.  The framework isthat of integration with respect to a function $g$ which iscontinuous but not necessarily of bounded variation. Here we shallcall these sets $g$-null. Since the family of $g$-null sets is a$\sigma$-ideal, the natural question is whether it is a family ofnull sets with respect to a Borel measure on the real line. Thepaper gives a negative answer to this question.

Publié le : 2012-01-01
DOI : https://doi.org/10.2478/tatra.v52i0.177 
@article{177,
     title = {Null sets with respect to a continuous function},
     journal = {Tatra Mountains Mathematical Publications},
     volume = {51},
     year = {2012},
     doi = {10.2478/tatra.v52i0.177},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/177}
}

Aversa, Vincenzo; De Simone, Anna. Null sets with respect to a continuous function. Tatra Mountains Mathematical Publications, Tome 51 (2012) . doi : 10.2478/tatra.v52i0.177. http://gdmltest.u-ga.fr/item/177/