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References in periodicals archive ?
A K-probability mean is a linear map [tau] : [D.sub.[tau]] [subset] [C.sup.0.sub.b] (X) [right arrow] K which is defined as the limit of barycenters with K-weights of a sequence of Borel probability measures on X; that is,
52) If f [member of] [S.sup.*], then there exists a Borel probability measure v on [partial derivative]D such that
To any measure [micro] [member of] P(R), we assign the Borel probability measure [[micro].sub.C] on C with
First, by applying a recently established criterion for subnormality of weighted composition operators in [L.sup.2]-spaces which makes no appeal to density of [C.sup.[infinity]]-vectors (see Theorem 1), we show that a densely defined weighted shift on a directed tree which admits a consistent system of probability measures (i.e., a system {[[mu].sub.v]}.sub.v[member of]V] Borel probability measures on [R.SUB.+] which satisfies (6)) is subnormal and, what is more, its nth power is densely defined if and only if all moments of these measures up to degree n are finite (cf.