Q19: What mathematical object is the posterior
Good evening,
trying to solve Q20, I realized I do not understand the mathematical nature of the prior/posterior. Your "definition" for the prior is P(h=f), but if h is a random variable with uniform distribution on [0,1] and f is some real number, the prior is just 0 for all f. The same holds of the posterior if the distribution of the random variable h conditioned by D is still of continuos nature.
My guess is that you are talking about h(f)'s density when asking questions about the properties of P(h=f  D) as a function. Is my guess correct?
