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A theorem on properties of sample functions of a random field and generalized random fields

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Abstract

We prove a theorem on the equivalence of some properties of a random field defined in terms of sample functions. We apply this theorem for studying generalized random fields.

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Correspondence to S. L. Starodubov.

Additional information

Original Russian Text © S.L. Starodubov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 7, pp. 48–56.

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Starodubov, S.L. A theorem on properties of sample functions of a random field and generalized random fields. Russ Math. 55, 40–46 (2011). https://doi.org/10.3103/S1066369X11070061

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Keywords and phrases

  • random fields
  • sample functions
  • total transform of measure
  • cylindric set algebras
  • generalized random field