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

5 votes
1 answer
137 views

CLT for a converging array of random variables

Assuming that for each fixed $k$, $(X_{n,1},\ldots,X_{n,k})\Longrightarrow(X_1,\ldots,X_k)$ where $X_1,\ldots,X_k$ are i.i.d. with mean zero and variance $\sigma^2$, will the array inherit the CLT f …