Independence, Essential Independence and Zero Correlation of Two Random Variables Condition on a Third.

In the paper the author defines, for constant regression which is called essential independence and zero correlation, analogues of Bell and Zimmers seven conditions. The author then extends and modifies their results. A salient point of the dissertation is that there are several seemingly distinct but logically equivalent ways of expressing constant regression. This equivalence connects local and global averaging probabilities. There is no similar observation to be made for zero correlation. On the other hand, there is an analogous, and even richer, collection of equivalent conditions for independence. This fact has been exploited by Bell and Zimmer and is adapted here. Modified author abstract