Probability and Measure Lecture 1: What is a Measure? 

In this case, nu(A) is a normalized counting measure. That is, it assigns to any A subset {1,2,...,n} the value |A|/n. Hence, if A = {1,...,n}, then nu(A) = 1. Here Omega is {1,...,n}. It sounds like you are trying to define a probability measure on the power set, i.e. some mu such that mu( 2^Omega )=1. In this case, we just want nu(Omega)=1. The power set, in this case, is the sigma-field of all 2^n measurable subsets of Omega.