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  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_ASCCC/Statistics%3A_UC_Davis/1%3A_Notes/1.12%3A_12_Convergence_in_distribution
    This is done by combining the compactness of the interval [0,1] (which implies that for any specific a\R we can always take a subsequence to make the sequence of numbers Fn(a) converge...This is done by combining the compactness of the interval [0,1] (which implies that for any specific a\R we can always take a subsequence to make the sequence of numbers Fn(a) converge to a limit) with a diagonal argument (for some enumeration r1,r2,r3, of the rationals, first take a subsequence to force convergence at r1; then take a subsequence of that subsequence to force convergence at r2, etc.; now form a subsequence whose k-th term is the \(k\…

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