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- W2056564671 abstract "In this paper it is proved that for a certain class of systems (systems of type (X)) one may construct a series (1)having the following properties:1) uniformly on the interval .2) For any measurable function on the interval and for any number , one can find a partial series from (1) which converges to almost everywhere on the set where is finite, and converges to in measure on .3) If, in addition, the functions () and are piecewise continuous and , then for all and It is shown that systems of type (X) include, for example, trigonometric systems, the systems of Haar and Walsh, indexed in their original or a different order, any basis of the space , and others.Bibliography: 19 items." @default.
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- W2056564671 date "1973-04-30" @default.
- W2056564671 modified "2023-09-26" @default.
- W2056564671 title "REPRESENTATION OF MEASURABLE FUNCTIONS ALMOST EVERYWHERE BY CONVERGENT SERIES" @default.
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- W2056564671 doi "https://doi.org/10.1070/sm1973v019n04abeh001791" @default.
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