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Mean quadratic convergence of signed random measures

Pierre Jacob, Paulo Eduardo Oliveira (1991)

Commentationes Mathematicae Universitatis Carolinae

We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.

Musielak-Orlicz spaces and prediction problems

Kazimierz Urbanik (2004)

Banach Center Publications

By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: X ( M ) = 0 1 e 2 π n i s M ( d s ) (n = 0,±1,...) The paper deals with prediction problems for sequences Xₙ(M) for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for Xₙ(M) (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö’s type...

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