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• Additive function
  ...unction (which way have meaning in say algebra), be sure to update the SET FUNCTION redirects that point into this page ...''[[real valued function|real valued]]'' [[set function]] on a class of [[set|sets]], {{M|\mathcal{A} }}, {{M|f:\mathcal{A}\rightarrow\mathbb{R} }} is ca
  6 KB (971 words) - 18:16, 20 March 2016
• Outer-measure/Definition
  </noinclude>An ''outer-measure'', {{M|\mu^*}} is a [[set function]] from a [[hereditary sigma-ring|hereditary {{sigma|ring}}]], {{M|\mathcal{ ...*(\bigcup_{n=1}^\infty A_n)\le\sum^\infty_{n=1}\mu^*(A_n)]}} - [[countably subadditive]]
  937 B (136 words) - 21:46, 8 April 2016
• Notes:Halmos measure theory skeleton
  # [[Measure]], {{M|\mu}}, countably additive extended real valued set function on a {{sigma|ring}}, {{M|\mathcal{R} }}, {{M|\mu:\mathcal{R}\rightarrow\bar ...e-measure]], {{M|\bar{\mu} }}, countably additive extended real valued set function defined on a ring of sets, {{M|\mathcal{R} }}, {{M|\bar{\mu}:\mathcal{R}\ri
  4 KB (581 words) - 20:31, 3 April 2016
• Notes:Measure theory plan
  ...}}) - Introduce a (positive) extended real valued [[countably additive set function]], {{M|\bar{\mu} }} on that ring. This will be a pre-measure and these are ...f every set in the ring, as well as being closed under countable union and set subtraction.
  4 KB (619 words) - 19:28, 24 May 2016
• Measure theory terminology doctrine
  ..., {{M|\bar{\mu} }} - ''[[extended real valued]]'' [[countably additive set function]] defined on a [[ring (measure theory)|ring]]. ...d]]'' [[countably subadditive set function|countably '''sub'''additive set function]] defined on a [[hereditary sigma ring|hereditary {{sigma|ring}}]]
  2 KB (232 words) - 03:57, 30 March 2016
• Notes:Halmos measure theory skeleton/Old page
  * [[additive set function]] ...M|\mu}} - [[extended real valued]], non negative, [[countably additive set function]] defined on a [[ring of sets]]
  4 KB (674 words) - 19:46, 3 April 2016
• Extending pre-measures to outer-measures
  ...{\mu} }}, on a [[ring of sets]], {{M|\mathcal{R} }}, we can define a new [[function]], {{M|\mu^*}} which is{{rMTH}}: ...infty A_n\right\} }} - here {{M|\text{inf} }} denotes the [[infimum]] of a set.
  11 KB (1,921 words) - 16:59, 17 August 2016
• Notes:The set of all mu*-measurable sets is a ring
  ...mathcal{H} }} and if {{M|\mathcal{S} }} is the set of all [[mu*-measurable set|{{M|\mu^*}}-measurable sets]] then {{M|\mathcal{S} }} is a [[sigma-ring]]. * I have proved that {{M|\mu^*\Big\vert_\mathcal{S} }} - the [[restriction (function)]] of {{M|\mu^*}} to {{M|\mathcal{S} }} - is a [[pre-measure]].
  4 KB (828 words) - 03:11, 30 May 2016