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@CarloBeenakker Almost. Marginalization tells you how to obtain p(x) from p(x,y) for some well-defined multivariate random variable (x,y). But I'm rather asking what is required of y in order for (x,y) to be well defined? E.g. should I define the probability space of y, and define the probability space of (x,y) as the product space of that of x and that of y? Or must y be defined on the same probability space as x? Obviously, I'm not well versed in the foundations of probability theory. I'm also asking about regularity conditions, although that is of less interest.
