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Let be a system of almost-everywhere finite measurable functions on that has one of the following properties: I. is a system for representing the functions in , , by convergent series.II. is a system for representing the functions in , , by almost-everywhere convergent series.III. has the strong Luzin -property.IV. can be multiplicatively completed to form a system for representing the functions in , , by series that converge in the -metric.It is shown that if is a system having one of the properties I-IV, then any subsystem of it with the form ( any natural number) also has this property.Bibliography: 9 titles. |
