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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.
##### MSC:
 46G10 Vector-valued measures and integration 28B05 Vector-valued set functions, measures and integrals 47B07 Linear operators defined by compactness properties