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• Formal logic language
  Formal logic plays an important role, especially so in set theory, but overall an important role. It is important to have a concrete understa
  2 KB (410 words) - 16:35, 9 March 2015
• Group
  A group is a set {{M|G}} and an operation <math>*:G\times G\rightarrow G</math>, denoted <ma If the operation is obvious then "Let {{M|G}} be the set of (whatever) and let {{M|(G,+)}} be a group"
  7 KB (1,332 words) - 07:17, 16 October 2016
• Cardinality
  Informally the cardinality of a set is the number of things in it. The cardinality of a set {{M|A}} is denoted <math>|A|</math>
  2 KB (327 words) - 10:25, 12 March 2015
• Well-ordering
  An ordering <math><</math> of a set {{M|P}} which is both: ...{{M|A\ne\emptyset}} has a least element. (Then {{M|A}} is ''[[Well-ordered set|well-ordered]]''<ref name="Top">Topology - James R. Munkres - 2nd edition</
  488 B (76 words) - 17:34, 24 July 2015
• Ring of sets
  Take a set {{M|X}}, the [[Power set|power set]] of {{M|X}}, {{M|\mathcal{P}(X)}} is a ring (further still, an [[Algebra o The empty set belongs to every ring
  2 KB (336 words) - 17:21, 18 August 2016
• Algebra of sets
  * [[Types of set algebras]] {{Measure theory navbox|plain}}
  3 KB (507 words) - 18:43, 1 April 2016
• Sigma-ring
  A non-empty class of sets {{M|S}} is a {{sigma|ring}} if<ref>Measure Theory, p24 - Halmos - Graduate Texts in Mathematics (18) - Springer</ref>: That is to say it is closed under [[Set subtraction|subtraction]] and [[Countable|countable]] [[Union|union]]
  728 B (125 words) - 15:34, 13 March 2015
• Sigma-algebra
  # Show a {{sigma|algebra}} is closed under [[set-subtraction]], {{M|\forall A,B\in\mathcal{A}[A-B\in\mathcal{A}]}} * {{M|\mathcal{A} }} is closed under [[Set subtraction|set subtraction]]
  8 KB (1,306 words) - 01:49, 19 March 2016
• Measure Theory
  ...generated by#Every set in R(A) can be finitely covered by sets in A|Every set in {{M|R(\mathcal{J}^n)}} can be finitely covered by sets in {{M|\mathcal{J But we do not know that every set in {{M|R(\mathcal{J}^n)}} can be finitely covered by DISJOINT sets in {{M|\
  4 KB (733 words) - 01:41, 28 March 2015
• Index of terms
  * Measure Theory | Refers to the set <math>\mathbb{R}\cup\{+\infty,-\infty\}</math> where it is understood that
  409 B (62 words) - 15:49, 13 March 2015
• Extended real value
  The set <math>\mathbb{R}\cup\{-\infty,+\infty\}</math> refers to "extended real val Halmos - Measure Theory - Page 1 - Spring - Graduate Texts in Mathematics (18)</ref>
  2 KB (396 words) - 16:07, 13 March 2015
• Set function
  ...] with a domain of definition that is a class of sets<ref>Halmos - Measure Theory - p30 - Springer - Graduate Texts in Mathematics (18)</ref> {{Definition|Set Theory|Measure Theory}}
  355 B (54 words) - 16:10, 13 March 2015
• Additive function
  {{Requires references|See Halmos' measure theory book too}} ...ve function (which way have meaning in say algebra), be sure to update the SET FUNCTION redirects that point into this page
  6 KB (971 words) - 18:16, 20 March 2016
• Pre-measure
  *# {{MM|1=\mu_0(\emptyset)=0}} - the measure of the empty set is {{M|0}} * {{MM|1=\mu_0(\emptyset)=0}} - the measure of the empty set is {{M|0}} and
  5 KB (782 words) - 01:49, 26 July 2015
• Measure
  A (positive) ''measure'', {{M|\mu}} is a [[set function]] from a [[sigma-ring|{{sigma|ring}}]], {{M|\mathcal{R} }}, to the ...n\right)=\sum_{n=1}^\infty\mu(A_n)]}} ({{M|\mu}} is a [[countably additive set function]])
  6 KB (941 words) - 14:39, 16 August 2016
• Measurable space
  {{Refactor notice|grade=A*|msg=Lets get this measure theory stuff sorted. At least the skeleton Given a [[set]], {{M|X}}, and a [[sigma-algebra|{{sigma|algebra}}]], {{M|\mathcal{A}\in\m
  2 KB (248 words) - 13:05, 2 February 2017
• Lebesgue measure
  The set function <math>\lambda^n:(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))\rightarro Where <math>\mathcal{J}=</math> the set of all half-open-half-closed 'rectangles' in <math>\mathbb{R}^n</math>
  804 B (129 words) - 00:28, 20 December 2016
• Semi-ring of sets/Definition
  A collection of {{plural|set|s}}, {{M|\mathcal{F} }}<ref group="Note">An F is a bit like an R with an un ...mS_i}}. We require that they be pairwise disjoint AND their union be the [[set difference]] of {{M|S}} and {{M|T}}.</ref> - this doesn't require {{M|S-T\i
  2 KB (337 words) - 17:25, 18 August 2016
• Ring generated by
  ===Every set in R(A) can be finitely covered by sets in A=== If {{M|A}} is any class of sets, then every set in {{M|R(A)}} can be covered by a finite union of sets in {{M|A}}
  2 KB (307 words) - 07:24, 27 April 2015
• Complement
  The complement of a set is everything not in it. For example given a set {{M|A}} in a space {{M|X}} the complement of {{M|A}} (often denoted {{M|A^c It may also be written using [[Set subtraction|set subtraction]]
  726 B (145 words) - 13:28, 18 March 2015