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Continuous mapping theorem

In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function, in Heine's definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The continuous mapping theorem states that…

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Continuous mapping theorem

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theorem xn continuous displaystyle probability convergence definition function random almost set arbitrary mathbb zero converges left geq right sequence therefore

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