Monotone class theorem: Difference between revisions

Revision as of 11:02, 18 July 2014

Revision as of 13:24, 6 August 2014

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===Statement===

Let <math>\mathcal{A}</math> be a [[Pi system|π-system]] that contains <math>\Omega\,</math> and let <math>\mathcal{H}</math> be a collection of real-valued functions from <math>\Omega</math> to '''R''' with the following properties:

(1) If <math>A \in \mathcal{A}</math>, then <math>\mathbf{1}_{A} \in \mathcal{H}</math>