Let G be a topological group, m be a G-valued finitely additive measure. Here strong boundedness is given in terms of G-neighbourhoods of 0. If m admits a finitely additive nonnegative real-valued measure which is equivalent to m then we say that it admits a control. As an application of a theorem concerning a general stochastic process in a finitely additive probability space, we prove that, if m is a strongly bounded finitely additive measure on P(Ω) with values in G admitting a control and if |Ω|≥max{c, the cardinality of the range of m}, then there is a subalgebra A of P(Ω) such that on it m is strongly bounded, countably additive and preserves the original range.
Stochastic processes and applications to countably additive restrictions of group-valued finitely additive measures
CANDELORO, Domenico;MARTELLOTTI, Anna
1996
Abstract
Let G be a topological group, m be a G-valued finitely additive measure. Here strong boundedness is given in terms of G-neighbourhoods of 0. If m admits a finitely additive nonnegative real-valued measure which is equivalent to m then we say that it admits a control. As an application of a theorem concerning a general stochastic process in a finitely additive probability space, we prove that, if m is a strongly bounded finitely additive measure on P(Ω) with values in G admitting a control and if |Ω|≥max{c, the cardinality of the range of m}, then there is a subalgebra A of P(Ω) such that on it m is strongly bounded, countably additive and preserves the original range.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
