An arithmetical examples of a non-Borel Luzin analytic set

M. A. Lunina

M. V. Lomonosov Moscow State University

Abstract: N. N. Luzin has constructed a sieve defining a screened non-Borel analytic set and has indicated the arithmetical properties of points of this set. In this article it is shown that a screened analytic set contains continuum number of points which do not have these arithmetical properties. Necessary and sufficient arithmetical conditions on points are found, under which they lie in a Luzin set screened by a sieve.

UDC: 517.5

Received: 30.11.1976

 English version: Mathematical Notes, 1977, 22:4, 783–788

Bibliographic databases:

• 
•