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Displaying similar documents to “Random sets and their asymptotic measure”

On a characterization of orthogonality with respect to particular sequences of random variables in L 2

Umberto Triacca, Andrei Volodin (2010)

Applications of Mathematics

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This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space L 2 ( Ω , , ) of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of L 2 ( Ω , , ) ) to be orthogonal to some other sequence in L 2 ( Ω , , ) . The result obtained...