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Linear transformations of orthogonal vector measures. Nondegenerated complete measures. (English. Ukrainian original) Zbl 0955.46023
Theory Probab. Math. Stat. 59, 153-159 (1999); translation from Teor. Jmovirn. Mat. Stat. 59, 148-155 (1998).
This work is devoted to some special problems of the theory of vector measures with values in a Hilbert space. Necessary and sufficient conditions are proposed in the paper under which the vector measure \(\mu\) has the representation \(\mu=a(\nu),\) where \(a\) is a bounded linear operator and \(\nu\) is an orthogonal vector measure.
46G10 Vector-valued measures and integration
28B05 Vector-valued set functions, measures and integrals
47B07 Linear operators defined by compactness properties