uniformly distributed
Let {un} be a sequence of real numbers. For 0≤α<β≤1 put
Z(N,α,β)=card{n∈[1..N]:α≤(unmod |
The sequence is uniformly distributed modulo if
for all . In other words a sequence is uniformly distributed modulo if each subinterval of gets its “fair share” of fractional parts of .
More generally, a sequence of points in a finite measure space is uniformly distributed with respect to a family of sets if
References
- 1 William Chen. Lectures on irregularities of point distribution. Available at http://www.maths.mq.edu.au/ wchen/ln.htmlhttp://www.maths.mq.edu.au/ wchen/ln.html, 2000.
-
2
Hugh L. Montgomery.
Ten Lectures on the Interface Between Analytic Number Theory
and Harmonic Analysis, volume 84 of Regional Conference Series in Mathematics. AMS, 1994. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0814.11001Zbl 0814.11001.
Title | uniformly distributed |
---|---|
Canonical name | UniformlyDistributed |
Date of creation | 2013-03-22 14:17:29 |
Last modified on | 2013-03-22 14:17:29 |
Owner | bbukh (348) |
Last modified by | bbukh (348) |
Numerical id | 6 |
Author | bbukh (348) |
Entry type | Definition |
Classification | msc 11K06 |
Classification | msc 11K38 |
Synonym | equidistributed |
Related topic | WeylsCriterion |