# regularity

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**Axiom of regularity**— In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo Fraenkel set theory and was introduced by harvtxt|von Neumann|1925. In first order logic the axiom reads::forall A (exists B (B in A)… …32

**Szemerédi regularity lemma**— In mathematics, Szemerédi s regularity lemma states that every large enough (finite undirected simple) graph can be approximated by a composition of a structured and a pseudo random part.Formal statement of the regularity lemmaThe formal… …33

**Castelnuovo–Mumford regularity**— In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space Pn is the smallest integer r such that it is r regular, meaning that whenever i > 0. The regularity of a subscheme is defined to be …34

**Statistical regularity**— is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers,… …35

**geometrical regularity**— noun a property of polygons: the property of having equal sides and equal angles • Syn: ↑regularity • Derivationally related forms: ↑regular (for: ↑regularity) • Hypernyms: ↑symmetry, ↑ …36

**Presumption of regularity**— The presumption of regularity[1] is a presumption that forms part of the law of evidence of England and Wales. It is expressed by the maxim of law[2] omnia praesumuntur rite et solemniter essa acta donec probetur in contrarium ,[3] which may be… …37

**maintenance of regularity**— index status quo Burton s Legal Thesaurus. William C. Burton. 2006 …38

**statistical regularity**— laws of statistics and probability used to predict events …39

**law of statistical regularity**— /ˌlɔ:r əv stəˌtɪstɪk(ə)l regjυ lærɪti/ noun a general rule that a group of people or objects taken from a larger group of people or objects will tend to resemble the larger group …40

**presumption of regularity**— The presumption, subject to rebuttal, that a public officer has performed his duty, acting in a regular and lawful manner. The rebuttable presumption that regulations, decisions, or orders of an administrative agency acting within the limits of… …