Let us use the word N-measure for nonnegative, finitely additive set functions defined on all subsets of the positive integers, equal to 0 on finite sets, and equal to 1 on the whole set. We say that the system Υ of sets determines the N-measure μ if any N-measure coinciding with μ on all elements of Υ is necessarily identical with μ.
Prove the existence of an N-measure μ that cannot be determined by a system of cardinality less than continuum.
I. Juhasz functionreal analysisreal analysis unsolved