Abstract. A theory of random Borel sets is presented, based on dyadic resolutions of compact metric spaces. The conditional expectation of the intersection of two independent random Borel sets is investigated. An example based on an embedding of Sierpiński's universal curve into the space of Borel sets is given. 2000

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The geodetic and astrometric potentialities of radiointerferometric “arc-method” are considered. This method is a logical generalization of differential astrometry method, achieved through the expulsion of all non-invariant with respect to 3 - dimensional rotations and non - constant in time parameters. The brief theory of method is given. An algorithme of processing of radiointerferometric information for the construction of a catalogue on arcs, cited as an example for two - element interferometer, is brought. The question of optimal interferometer’s base orientations and observational regimes has been studied analytically. The estimations of accuracy are given for the determination geodesic and geodynamical parameters through the standard arcs. The question of application of arc - method for verification of relativistic gravitation theories is discussed.

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