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• Tuple
  * Countably infinite tuples
  610 B (97 words) - 16:30, 23 August 2015
• Additive function
  ===Countably additive=== With the same definition of {{M|f}}, we say that {{M|f}} is ''countably additive'' if for a [[pairwise disjoint]] family of sets {{M|1=\{A_n\}_{n=1
  6 KB (971 words) - 18:16, 20 March 2016
• Pre-measure
  ...ion already, so we can measure over that. We then extend this to countably infinite.</ref>: ...nfinite'' unions that are not closed on an ''algebra''. There are ''some'' infinite unions which are however in the union.
  5 KB (782 words) - 01:49, 26 July 2015
• Index of properties
  | closed under [[Countably infinite|countably infinite]] intersection. <math>\forall (A_n)_{n=1}^\infty\subseteq\mathcal{A}[\cap_{ | closed under [[Countably infinite|countably infinite]] union. <math>\forall (A_n)_{n=1}^\infty\subseteq\mathcal{A}[\cup_{n=1}^\i
  2 KB (360 words) - 20:43, 15 June 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
  ...is a finite [[sequence]], in this case we shall consider the ''[[countably infinite]]'' [[sequence]]: ...es (as we implicitly associate each finite sequence with the corresponding infinite sequence by the above construction) ({{WLOG}})
  4 KB (688 words) - 21:03, 31 July 2016
• Every sequence in a compact space is a lingering sequence/Proof
  ...\infty\subseteq (x_n)_{n=1}^\infty}} and a sequence contains a [[countably infinite]] amount of terms. As [[a subset has cardinality less than or equal to a se # This is obviously a contradiction, as there are countably many terms of the sequence in the space!
  2 KB (452 words) - 16:46, 6 December 2015
• Limsup and liminf (sequence of sets)
  ...{M|(A_n)}} is the set that contains {{M|x\in X}} given that {{M|x}} is in (countably) infinitely many elements of the sequence. ...e same. This is because an element can ''both'' be in ''and'' not be in an infinite number of elements!
  2 KB (386 words) - 22:17, 19 April 2016
• 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/Statement
  * for all {{M|A\in\mathcal{R} }} and for all ''[[countably infinite]]'' or ''[[finite]]'' [[sequence|sequences]] {{M|(A_i)\subseteq\mathcal{R} ...re {{M|\bigcup_i A_i\in\mathcal{R} }} which isn't guaranteed for countably infinite sequences)<noinclude>
  801 B (129 words) - 20:44, 31 July 2016
• Extending pre-measures to outer-measures
  #*#** Given a set {{M|A}} and a [[countably infinite]] or [[finite]] ''[[sequence]]'' of sets, {{M|(A_i)}} such that {{M|A\subse # {{Warning|I never consider the case where a measure measures a set to be infinite. Where this happens things like {{M|\infty<\infty}} make no sense}}
  11 KB (1,921 words) - 16:59, 17 August 2016
• Types of set algebras/Type table
  ...}}<ref group="Note" name="sigma-U-closed">closed under finite or countably infinite union</ref>
  4 KB (573 words) - 20:00, 19 August 2016