21 we often write this as plim n g w n g plim n w n

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We often write this as plim n g W n g plim n W n so we can pass the probability limit through continuous functions. Notice this contains the usual result on convergence for nonrandom sequences: lim n g a n g lim n a n if a n a and g  is continous at a . Slutsky’s Theorem has many applications in large-sample statistical analysis. 22
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