Induced Measures and Product Measures

  title={Induced Measures and Product Measures},
  author={Michel Simonnet},
9.1 Let µ be a measure on a semiring S whose underlying set is X. Let Y be a µ-measurable subset of X. Let T be a semiring whose underlying set is Y. Assume that µ, Y, and T are endowed with adequate properties. We define the measure µ/ T induced by µ on T and see how to integrate with respect to this induced measure (Theorem 9.1.1).