Inner variation and the SLi-functions
Julius V. Benitez, Recson G. Canton · International Journal of Mathematical Analysis · 2015
article distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we investigate the Lusin Condition’s by utilizing the concept of δ-fine. Using concepts of covering relations and inner varia-tion, we gave an easier way of studying Lusin’s condition (N). Impor-tant results regarding full and fine covering relations are presented to help build the concept of inner variation zero. Inner variation zero gives an alternative approach to measure zero independent to the theory of Lebesgue measure. We use these concepts to define SLi-functions and give some results related to absolutely continuous functions, functions having negligible variations and functions satisfying the strong Lusin conditions.