Conditional Probability Distributions in the Wide Sense 1

  title={Conditional Probability Distributions in the Wide Sense 1},
  author={Lester E. Dubins},
Introduction. Doob [3, p. 29],2 has shown that if ()= [U, 11, u] is a probability space (i.e. 11 is a cr-field of subsets of a set U and u is a countably additive non-negative measure defined on 11, normalized by the condition u(U) = l) and 1l0 is a o--subfield of 11, and y is an re-dimensional random variable mapping U into an re-dimensional Euclidean space X, then y possesses a conditional distribution in the wide sense relative to llo. More specifically, he proved the existence of a function… CONTINUE READING