On the range of semigroup valued measures
ISSN: 0010-0757
Ano de publicación: 1984
Volume: 35
Fascículo: 1
Páxinas: 71-83
Tipo: Artigo
Outras publicacións en: Collectanea mathematica
Resumo
It is proved that every measure with values in a topological semigroup, whose topology is defined by a family of semi-invariant in zero pseudometrics, is bounded (in some sence) i fit is $s$-bounded or it is $\sigma$-additive and the pseudometrics are invariant in zero, in the second casi it also proved that the range of the mesaure is conditionally compact. Moreover it is stated that the range of a $\sigma$-additive measure with values in a topological semigroup (of the last type) is compact if the measure is purely atomic and of bounded variation. Some results about the uniform boundness of a sequence of semigroup valued measures and group, are proved.\newline\newline AMS (MOS) Subject classification$\cdots$ 28B10