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Note that the indicator function <math>\mathbf{1}_{f^{-1}(B)}</math> is <math>\mathcal{A}</math>-measurable for all <math>B \in \mathcal{B}</math> iff <math>f</math> is measurable.
This example allows us to think of a Markov kernel as a generalised function with a (in general) random rather than certain value. That is, it is a [[multivalued function]] where the values are not equally weighted.
===[[Galton–Watson process]]===
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