If ( is countable and is defined on P(() by (A) number of points of A, show that is a measure Furthermore, is finite or finite, depending on whether ( is finite or denumerable, respectively (This measure is called the counting measure ) ...

If is finite then is 0 0 and finitely additive since there are only f ...

If ( is countable and is defined on P(() by: (A) = number of points

Question:

If ( is countable and μ is defined on P(() by: μ (A) = number of points of A, show that μ is a measure. Furthermore, μ is finite or σ-finite, depending on whether ( is finite or denumerable, respectively. (This measure is called the counting measure.)