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Convergence of series, sequences and functions and different modes of convergence.

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It is not true in general. If $Z_t$ is not bounded, the expectation can diverge to infinity. For example, define: $$ Z_t = \left\{\begin{array}{lc}2^{2^{t}} & \text{with probability $\epsilon/2$}\\ …
answered May 24 '17 by N. Gast