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• Properties of classes of sets closed under set-subtraction
  Suppose {{M|\mathcal{A} }} is an arbitrary class of [[set|sets]] with the property that: ...=\forall A,B\in\mathcal{A}[A-B\in\mathcal{A}]}} where {{M|A-B}} denotes "[[set subtraction]]" ({{AKA}}: [[relative complement]])
  3 KB (490 words) - 11:38, 21 August 2016
• Sigma-algebra generated by
  See [[Notes:Just what is in a generated sigma-algebra|Just what is in a generated {{Sig ...set|power set]] of {{M|\Omega}}) there exists<ref name="PTACC">Probability Theory - A Comprehensive Course - Second Edition - Achim Klenke</ref> a smallest [
  2 KB (286 words) - 22:02, 17 March 2016
• Partition (abstract algebra)
  ...ry [[Indexing set|indexing set]], to each element {{M|i\in I}} we assign a set {{M|A_i}} which is non-empty. If: ...Analysis - Part 1: Elements - Krzystof Maurin</ref> ''the partition of the set {{M|B}} into classes {{M|A_i}} for {{M|i\in I}}''
  2 KB (316 words) - 16:03, 18 June 2015
• Group action
  A (left) ''group action'' of a [[group]] {{M|(G,*)}} on a [[set]] {{M|X}} is a [[mapping]]{{rAAPAG}}: ** [[The symmetric group on a set acts on the set by evaluation]]
  2 KB (320 words) - 23:28, 21 July 2016
• Dynkin system generated by
  Given a set {{M|X}} and another set {{M|\mathcal{G}\subseteq\mathcal{P}(X)}} which we shall call the ''generato {{Todo|Be bothered, notes on p75 of my notebook, or page 31 of<ref name="MIM"/>}}
  2 KB (245 words) - 15:16, 16 December 2016
• Well-ordered set
  A set {{M|A}} with an [[Linear ordering|linear ordering]] {{M|<\subseteq A\times ==Notes==
  916 B (164 words) - 17:49, 24 July 2015
• Dynkin system
  * [[Types of set algebras]] ==Notes==
  1 KB (184 words) - 01:54, 19 March 2016
• Dynkin system/Definition 2
  <noinclude>{{Extra Maths}}</noinclude>Given a set {{M|X}} and a family of subsets of {{M|X}} we denote {{M|\mathcal{D}\subset ==Notes==
  719 B (120 words) - 23:22, 2 August 2015
• Function terminology
  ...ion {{M|f:A\rightarrow B}} where {{M|A}} and {{M|B}} are assumed to be any set unless stated otherwise we say the following about {{M|f}}: ==Notes==
  1 KB (165 words) - 02:07, 3 August 2015
• Borel sigma-algebra generated by
  ...used, however in measure theory this notation is often used to denote the set of half-open-half-closed rectangles in {{M|\mathbb{R}^n}} - a totally separ ==Notes==
  2 KB (244 words) - 08:30, 6 August 2015
• Borel sigma-algebra
  ...illing</ref>. It is [[Sigma-algebra generated by|generated by]] the [[Open set|open sets]] of the [[Metric space|metric space]] {{M|(\mathbb{R},\vert\cdot ...">Conventionally, {{M|\mathcal{J} }} denotes the open sets, but in measure theory this seems to denote the sets of half-open-half-closed rectangles, and it i
  5 KB (854 words) - 09:25, 6 August 2015
• The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set
  ...than the sum of the (pre-)measures of the elements of a covering for that set/Statement|Statement]]== ...than the sum of the (pre-)measures of the elements of a covering for that set/Statement}}
  4 KB (688 words) - 21:03, 31 July 2016
• Category
  # For every ordered pair, {{M|(X,Y)}} of ''objects'' a set {{M|\hom(X,Y)}} of ''morphisms'' {{M|f}} ==Notes==
  2 KB (347 words) - 00:36, 27 September 2015
• Classes of continuously differentiable functions
  Given {{M|U\subseteq\mathbb{R}^n}} (where {{M|U}} is [[Open set|open]]) and some {{M|k\ge 0}}, a function of the form: ...''"...functions of class {{M|C^k}} on {{M|U}} by..."'' when describing the set {{M|C^k(U)}}</ref> we require<ref name="ITSM"/>:
  3 KB (632 words) - 20:32, 16 October 2015
• Pre-measure/New page
  ...ive) pre-measure'' is an ''[[extended real valued]]'' [[countably additive set function]], {{M|\bar{\mu}:\mathcal{R}\rightarrow\overline{\mathbb{R}_{\ge 0 * [[Types of set algebras]]
  3 KB (422 words) - 21:25, 17 August 2016
• Subsequence/Definition
  {{Requires cleanup|grade=A|msg=The notes are a bit messy}} ==Notes==
  3 KB (484 words) - 21:54, 16 November 2016
• Cartesian product
  Given two sets, {{M|X}} and {{M|Y}} their ''Cartesian product'' is the set: ===Set construction===
  2 KB (318 words) - 14:25, 19 February 2016
• Strict partial ordering
  ...for anything other than denoting [[subset|subsets]], the relation and the set it relates on will go together, so you'll already be using {{M|\subseteq}} ==Notes==
  3 KB (436 words) - 10:15, 20 February 2016
• Preorder
  A ''preorder'', {{M|\preceq}}, on a set {{M|X}} is a [[relation]] in {{M|X}}, so {{M|\preceq\subseteq X\times X}}, A tuple, consisting of a set {{M|X}}, equipped with a preorder {{M|\preceq}} is called a ''[[preset]]''<
  2 KB (355 words) - 10:13, 20 February 2016
• Index of operators on ordered sets
  If you are given a set, say {{M|X}} and any of a: on that set, then this page indexes various operators that might take such a structured
  2 KB (304 words) - 17:01, 20 February 2016