Before revision:  With an additional\texttt{  Strong-Law-type assumption, we show that the total number of file fetches under \texttt{LeadCache} remains almost surely finite .
After revision:  With an additional\texttt{ policy, one based on Pipage rounding and the other based on Madow's sampling, each of which makes precisely one call to an LP-solver per iteration. With a Strong-Law-type assumption, we show that the total number of file fetches under \texttt{LeadCache} remains almost surely finite .