Let ( be an infinite set (countable or not) and let A be the discrete field Let 1, 2, ( (, and with each n, associate a nonnegative number pn (such that ((n 1 pn () On A, define the set function by (A) (n(A Pn Then show that is a measure on A ...

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Let ( be an infinite set (countable or not) and let A be the discrete -field. Let

Question:

Let ( be an infinite set (countable or not) and let A be the discrete σ-field. Let {ω1, ω2,...} ( (, and with each ωn, associate a nonnegative number pn (such that ((n=1 pn ≤ (). On A, define the set function μ by: μ(A) = (ωn(A Pn. Then show that μ is a measure on A.