Question

the measure of set of integers z is​

Answer 1

➡ Let m be the counting measure on the set of all integers Z. If µ is any measure on Z, then there is a non-negative function f on Z such that µ(E) = ∫E f(x)dm(x) for any subset E of Z.

Answer 2

Step-by-step explanation:

There is an exercise in my text that tells me to prove the "obvious and easy to see" fact that Z and Q have measure zero.

There is an exercise in my text that tells me to prove the "obvious and easy to see" fact that Z and Q have measure zero.Er...here is what I know so far. If I have an interval, then the measure is the end point subtracting the initial point i.e. the length of that interval. What can I do to extend this line of thinking to Z and Q and any countable set?