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Probability and Stochastic Processes by Ionut Florescu

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7.3 Continuous Mapping Theorem. Joint Convergence. Slutsky's Theorem

The theorem above is also true even if g is discontinuous at certain points c07-math-0547 with the condition that c07-math-0548. We will not prove this theorem: two of the assertions we have proved earlier, and the convergence in probability implication is very simple.

In general, ...

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