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Can anyone point me a book where it has a proof of Theorem 1.7 (ii) of Jun Shao's book - Mathematical Statistics? I need this to show that given a distribution on one space and a collection of conditional distributions (which are conditioned on values of the first space) on another space, I can construct a joint distribution in the product space. There is a print of the theorem below. enter image description here

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  • $\begingroup$ It seems to be a direct application of Carathéodory's extension theorem. $\endgroup$ – Saad Mar 25 at 15:46
  • $\begingroup$ I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution. $\endgroup$ – Ga13 Mar 25 at 16:27
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After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)

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