|
|
| Line 1: |
Line 1: |
| − |
| |
| − |
| |
| | ==Definition== | | ==Definition== |
| − | The set function <math>\lambda^n:(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))\rightarrow\mathbb{R}_{\ge}</math><ref>P27 - Measures, Integrals and Martingales - Rene L. Schilling</ref> that assigns every half-open rectangle <math>[[a,b))=[a_1,b_1)\times\cdots\times[a_n,b_n)\in\mathcal{J}</math> as follows:
| + | we measure a paper called lebesgue with our friends |
| − | | + | |
| − | <math>\lambda^n\Big([[a,b))\Big)=\Pi^n_{i=1}(b_i-a_i)</math>
| + | |
| − | | + | |
| − | Where <math>\mathcal{J}=</math> the set of all half-open-half-closed 'rectangles' in <math>\mathbb{R}^n</math>
| + | |
| − | | + | |
| − | Note that it can be shown <math>\mathcal{B}(\mathbb{R}^n)=\sigma(\mathcal{J})</math> where <math>\sigma(\mathcal{J})</math> is the [[Sigma-algebra|{{Sigma|algebra}}]] [[Sigma-algebra generated by|generated by]] <math>\mathcal{J}</math>
| + | |
| − | | + | |
| | {{Definition|Measure Theory}} | | {{Definition|Measure Theory}} |
| | ==References== | | ==References== |
Revision as of 07:43, 23 August 2015
Definition
we measure a paper called lebesgue with our friends
References
