Difference between revisions of "Pre-measure/Properties in common with measure"
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| − | {{Begin Inline Theorem}} | + | <noinclude>{{Extra Maths}}</noinclude>{{Begin Inline Theorem}} |
* '''Finitely additive:''' if {{M|1=A\cap B=\emptyset}} then {{M|1=\mu_0(A\udot B)=\mu_0(A)+\mu_0(B)}} | * '''Finitely additive:''' if {{M|1=A\cap B=\emptyset}} then {{M|1=\mu_0(A\udot B)=\mu_0(A)+\mu_0(B)}} | ||
{{Begin Inline Proof}} | {{Begin Inline Proof}} | ||
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{{End Proof}}{{End Theorem}} | {{End Proof}}{{End Theorem}} | ||
{{Begin Inline Theorem}} | {{Begin Inline Theorem}} | ||
| − | * If {{M|A\subseteq B}} and {{M|\mu_0(A)<\infty}} then {{M|\mu_0(B-A)=\mu_0(B)-\mu(A)}} | + | * If {{M|A\subseteq B}} and {{M|\mu_0(A)<\infty}} then {{M|1=\mu_0(B-A)=\mu_0(B)-\mu(A)}} |
{{Begin Inline Proof}} | {{Begin Inline Proof}} | ||
{{Todo|Be bothered, note the significance of the finite-ness of {{M|A}} - see [[Extended real value]]}} | {{Todo|Be bothered, note the significance of the finite-ness of {{M|A}} - see [[Extended real value]]}} | ||
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{{Begin Inline Proof}} | {{Begin Inline Proof}} | ||
{{Todo|Again - be bothered}} | {{Todo|Again - be bothered}} | ||
| − | {{End Proof}}{{End Theorem}} | + | {{End Proof}}{{End Theorem}}<noinclude> |
| + | ==Notes== | ||
| + | <references group="Note"/> | ||
| + | ==References== | ||
| + | <references/> | ||
| + | {{Theorem Of|Measure Theory}} | ||
| + | </noinclude> | ||
Latest revision as of 22:30, 30 March 2016
Notes
- Jump up ↑ Sometimes stated as monotone (it is monotone in Measures, Integrals and Martingales in fact!)
References
