Suppose we are given a set $F =\{f|\ f:\mathbb{R} \to \mathbb{R}\}$, i.e. an arbitrary set (not sure about its countablility) of real-valued functions. What is the probability, that a function $f_k$, chosen at random from the set is Riemann Integrable?
Note: I came up with this problem entirely on my own. So, if there are any "loose-statements", please correct it. I don't have enough knowledge to even approach this. There might be some duplicates out there, which I am not sure of. Is this even a valid question?
Thank you.