Difference between revisions of "Pre-image sigma-algebra"
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Revision as of 16:49, 17 July 2015
Let [ilmath]f:X\rightarrow X'[/ilmath] and let [ilmath]\mathcal{A}'[/ilmath] be a [ilmath]\sigma[/ilmath]-algebra on [ilmath]X'[/ilmath], we can define a sigma algebra on [ilmath]X[/ilmath], called [ilmath]\mathcal{A} [/ilmath], by:
- [ilmath]\mathcal{A}:=f^{-1}(\mathcal{A}'):=\left\{f^{-1}(A')\vert\ A'\in\mathcal{A}'\right\}[/ilmath]
TODO: Measures Integrals and Martingales - page 16
