| 词条 | Discrepancy theory |
| 释义 |
In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (mostly geometrically defined) subsets. The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one. Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity. A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval.{{citation needed|date=January 2018}} TheoremsDiscrepancy theory is based on the following classic theorems:
Major open problemsThe unsolved problems relating to discrepancy theory include:
ApplicationsApplications for discrepancy theory include:
See also
References1. ^{{cite journal | title = "Integer-making" theorems | journal = Discrete Applied Mathematics | volume = 3 | issue = 1 | doi = 10.1016/0166-218x(81)90022-6 | author = József Beck and Tibor Fiala | pages=1–8}} 2. ^{{cite journal|title = Six Standard Deviations Suffice|author = Joel Spencer|authorlink = Joel Spencer|journal = Transactions of the American Mathematical Society|volume = 289|issue = 2|date=June 1985|pages = 679–706|doi = 10.2307/2000258|publisher = Transactions of the American Mathematical Society, Vol. 289, No. 2|jstor = 2000258}} Further reading
4 : Diophantine approximation|Unsolved problems in mathematics|Combinatorics|Measure theory |
| 随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。