Lebesgue measure
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Definition
The set function [math]\lambda^n:(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))\rightarrow\mathbb{R}_{\ge}[/math][1] 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:
[math]\lambda^n\Big([[a,b))\Big)=\Pi^n_{i=1}(b_i-a_i)[/math]
References
- ↑ P27 - Measures, Integrals and Martingales - Rene L. Schilling
