Improper priors are generally only considered in the case of continuous distributions so ‘sum’ is probably not the right term, integrate is usually used.
I used the term ‘weight’ to signify an integral because of how I usually intuit probability measures. Say you have a random variable X that takes values in the real line, the probability that it takes a value in some subset S of the real line would be the integral of S with respect to the given probability measure.
No problem.
Improper priors are generally only considered in the case of continuous distributions so ‘sum’ is probably not the right term, integrate is usually used.
I used the term ‘weight’ to signify an integral because of how I usually intuit probability measures. Say you have a random variable X that takes values in the real line, the probability that it takes a value in some subset S of the real line would be the integral of S with respect to the given probability measure.
There’s a good discussion of this way of viewing probability distributions in the wikipedia article. There’s also a fantastic textbook on the subject that really has made a world of difference for me mathematically.