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On strong uniform distribution IV
Journal of Inequalities and Applications volume 2005, Article number: 639193 (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.
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Nair, R. On strong uniform distribution IV. J Inequal Appl 2005, 639193 (2005). https://doi.org/10.1155/JIA.2005.319
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DOI: https://doi.org/10.1155/JIA.2005.319