We introduce the notion of regular and purely irregular charges with respect to a pair of pavings and study their structural properties. Moreover, we link regularity and σ-additivity, obtaining some generalizations of well-known theorems. Finally, when the pavings satisfy some reasonable weak conditions, we can decompose any bounded charge into regular and purely irregular decomposants; this decomposition becomes the Hewitt-Yosida one, whenever the charges are defined on the Baire σ-field of a countably compact space.
Regular and purely irregular bounded charges: a decomposition theorem
GIROTTO, BRUNO;HOLZER, SILVANO
1992-01-01
Abstract
We introduce the notion of regular and purely irregular charges with respect to a pair of pavings and study their structural properties. Moreover, we link regularity and σ-additivity, obtaining some generalizations of well-known theorems. Finally, when the pavings satisfy some reasonable weak conditions, we can decompose any bounded charge into regular and purely irregular decomposants; this decomposition becomes the Hewitt-Yosida one, whenever the charges are defined on the Baire σ-field of a countably compact space.File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
