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How about this: Let $G(t) = \nu(0,t).$ Let $N_t$ be the cardinality of $\{n: S_n\le G(t)\}.$$\{n: S_n\le \nu(0,t)\}.$
How about this: Let $G(t) = \nu(0,t).$ Let $N_t$ be the cardinality of $\{n: S_n\le G(t)\}.$
How about this: Let $N_t$ be the cardinality of $\{n: S_n\le \nu(0,t)\}.$
