https://www.cs.cmu.edu/~15850/handouts/matousek-vondrak-prob-ln.pdf https://www.cs.cmu.edu/~15850/handouts/matousek-vondrak-prob... Here is a good technical in

https://www.cs.cmu.edu/~15850/handouts/matousek-vondrak-prob-ln.pdf https://www.cs.cmu.edu/~15850/handouts/matousek-vondrak-prob... Here is a good technical introduction to the probabilistic method, which verifies everything I've written (in the same language as I've used too, namely that of measures and probability spaces, which is the standard in modern mathematics for formalising this stuff). In particular, I quote: > We would like to prove the existence of a combinatorial object with specified properties. Unfortunately, an explicit construction of such a “good” object does not seem feasible, and maybe we do not even need a specific example; we just want to prove that something “good” exists. Then we can consider a random object from a suitable probability space and calculate the probability that it satisfies our conditions. If we prove that this probability is strictly positive, then we conclude that a “good” object must exist; if all objects were “bad”, the probability would be zero. I also quote (emphasis mine): > 1.1.2 Definition (Random graphs). 6 The probability space of random graphs G(n, p) is a finite probability space whose elementary events are all graphs on a fixed set of n vertices.