Accession Number : AD0722381

Title :   On a Theorem of Weyl,

Corporate Author : CENTER FOR NAVAL ANALYSES ARLINGTON VA

Personal Author(s) : Rogers,Warren F.

Report Date : MAR 1971

Pagination or Media Count : 23

Abstract : If A is a Lebesque measurable subset of the interval (0,1) and t is any irrational number in that interval, then by a well-known theorem of Weyl, the frequency with which the integer products of t modulo one fall in A converges to the measure of A. This result may be used to evaluate asymptotic error in certain approximations. For a special case, Weyl's theorem is shown to extend to rational numbers t and a lower bound on frequency is derived. (Author)

Descriptors :   (*APPROXIMATION(MATHEMATICS), ERRORS), MEASURE THEORY, SET THEORY, COMPLEX NUMBERS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE