## Abstract

A sequence s 1, s 2, … $ s_1, s_2,\ldots $ in U = [ 0, 1) $ { \text{ U}}=[0,1) $ is said to be uniformly distributed if, in the limit, the number of s j $ s_j $ falling in any given subinterval is proportional to its length. Equivalently, s 1, s 2, … $ s_1, s_2,\ldots $ is uniformly distributed if the sequence of equiweighted atomic probability measures µ N (s j) = 1 / N $ \mu _N(s_j)=1/N $, supported by the initial N-segments s 1, s 2, …, s N $ s_1, s_2,\ldots, s_N $, converges weakly to Lebesgue measure on U $ {{ \text{ U}}} $. This notion immediately generalizes to any topological space with a corresponding probability measure on the Borel sets.

Original language | English (US) |
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Title of host publication | Handbook of Discrete and Computational Geometry, Third Edition |

Publisher | CRC Press |

Pages | 331-357 |

Number of pages | 27 |

ISBN (Electronic) | 9781498711425 |

ISBN (Print) | 9781498711395 |

DOIs | |

State | Published - Jan 1 2017 |

## All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)