
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 wellknown 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