σ-finite and semimoderate variational measures

Absolutely continuous variational measures of Mawhin’s type

“…At the same time, σ-finiteness of a variational measure gives some information about differentiability properties of the set function that determines this measure (see [2,4,6,7,10,13,21,24,32,35,36,40,41,42,44,49]). It is also well-known that, unlike general situation, the absolute continuity of a variational measure implies its σ-finiteness (see [3,4,6,7,9,12,14,15,17,19,27,31,33,36,39,40,44,46,47,49]). This relation between the absolute continuity and σ-finiteness motivated several authors to find characterizations of σ-finite variational measures.…”