Open Access

On strong uniform distribution IV

Journal of Inequalities and Applications20052005:639193

DOI: 10.1155/JIA.2005.319

Received: 24 January 2003

Published: 11 July 2005

Abstract

Let be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on . Let denote the fractional part of the real number . We say that is an sequence if for each we set , then , almost everywhere with respect to Lebesgue measure. Let . In this paper, we show that if is an for , then there exists such that if denotes , . We also show that for any sequence and any nonconstant integrable function on the interval , , almost everywhere with respect to Lebesgue measure.

Authors’ Affiliations

(1)
Department of Mathematical Sciences, The University of Liverpool

Copyright

© Nair 2005