BV-functions on semilattices

𝐵𝑉-functions on commutative semigroups

“…If S is a semilattice, then the above corollary implies the equivalence between our notion and that introduced in [3]. The equivalence between our concept and that of [5] (as well as the classical concept for linearly ordered sets) follows routinely once the latter is formulated in our setting.…”

“…The equivalence between our concept and that of [5] (as well as the classical concept for linearly ordered sets) follows routinely once the latter is formulated in our setting. If S is a distributive lattice and ƒ is a BV-valuation, then it follows from [3] that V(f) is the total variation as defined in [1].…”

“…[3], [4] and [5]). Here, using different techniques, we further extend this notion to commutative semigroups with identity and show that the BK-functions characterize the "abstract moment sequences" or what we call moment functions.…”

Moment and BV-Functions on Commutative Semigroups

“…However, the BV-functions of [4] were seen to be the functions in E {S) and the total variation in that sense of such a function was also seen DO to be f ,. e (o) d\p, |.…”

“…License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use A formally different notion of total variation of functions on a semilattice was introduced in [4]. However, the BV-functions of [4] were seen to be the functions in E {S) and the total variation in that sense of such a function was also seen DO to be f ,.…”