In the context of the proof of Theorem 4.8 prove that [liminf _{n ightarrow infty} F_{n}(x) geq
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In the context of the proof of Theorem 4.8 prove that
\[\liminf _{n ightarrow \infty} F_{n}(x) \geq F(x-\varepsilon) .\]
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Theorem 4.8. Let {X} be a sequence of random variables that converge in probability to a random variable X as noo. Then X, X as n .
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