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Definition: Measureable Function
Let \((M,{\mathcal {A}})\) und \((N,{\mathcal {B}})\) be two measurable sets. A function \(\varphi \colon M\longrightarrow N\,\) is called measureable (or \({\mathcal {A}}{\mathcal {B}}\)measureable), if for all \(T\in {\mathcal {B}}\) the inverse image \(\varphi ^{1}(T)\) is in \({\mathcal {A}}\).
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of OsnabrÃ¼ck