Question: Let (S, d) be a metric space, and u be a probability measure defined on (S, B(S)), where B(S) denotes the Borel o-algebra on S.

Let (S, d) be a metric space, and u be a probability measure defined on (S, B(S)), where B(S) denotes the Borel o-algebra on S. Use the monotone class theorem to show that Co(S) is dense in Cl (S, B(S), u), i.e. for each fe C](S, B(S), u) there exists a sequence (fn)n>1 in Co(S'), such that limn +co fs If-fn|du = 0
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