Let ( = {0, 1, 2,....}, let A be the discrete -field of subsets of (, and

Let ( = {0, 1, 2,....}, let A be the discrete σ-field of subsets of (, and on A, define the function μ by: μ(A) = number of nonnegative integers in A. Then show that μ is a measure, and indeed, a σ-finite measure.