MathDB

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

\Upsilon

of sets determines the

N

-measure

\mu

if any

N

-measure coinciding with

\mu

on all elements of

\Upsilon

is necessarily identical with

\mu

. Prove the existence of an

N

-measure

\mu

that cannot be determined by a system of cardinality less than continuum. I. Juhasz

Problem Statement