Talk:Relative Frequency is Probability Measure

I'd like to keep the induction proof in, for the same reason students are taught the induction proof for Closed Form for Triangular Numbers even though the direct proof is much easier. This theorem an amateur mathematician like me would be exposed to at the very beginning of a course in probability. I've also never seen Gemgignani's trick before of going back to the base case (hey, that's cheating!)
 * Standard technique - apply the base case to the induction hypothesis to go from n to n+1. Lots of the proofs on this site use it. --prime mover 09:18, 9 December 2011 (CST)

... But I defer my decision to PW veterans. (This isn't quite Gemignani's proof, he's proving something similar). Is the proof you were thinking of PM this one? Additive and Countably Subadditive Functions are Countably Additive --GFauxPas 08:11, 9 December 2011 (CST)
 * That's the one. The inductive proof is all very well I suppose, but it's a bit handwavey. Might be best to extract that particular part of the proof into its own page so we can hack it to pieces at will. At the moment, sitting as part 3 of a multi-part proof, it's less easy to take liberties with. --prime mover 09:10, 9 December 2011 (CST)
 * ... maybe it's not handwavey as such, but I think we might tighten up the language in the description of the base case. Not sure yet, haven't got a braincell spare to think about it. --prime mover 09:12, 9 December 2011 (CST)
 * My Calc I professor (he teaches many types of math) was kind enough to look it over for me, and he said the proof works. I'll see if I can make the language better. --GFauxPas 09:28, 9 December 2011 (CST)