Accession Number:

AD0722381

Title:

On a Theorem of Weyl,

Descriptive Note:

Corporate Author:

CENTER FOR NAVAL ANALYSES ARLINGTON VA

Personal Author(s):

Report Date:

1971-03-01

Pagination or Media Count:

23.0

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, Weyls theorem is shown to extend to rational numbers t and a lower bound on frequency is derived. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE