If $X_n$ converges to $X$ almost surely how can we prove that $\cfrac 1{X_n}$ will converge to $\cfrac 1{X}$ almost surely?
If $X_n$ converges to $X$ almost surely how can we proof that $1/X_n$ will converge to $1/X$ almost surely?
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sequences-and-series
analysis
convergence-divergence
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1The limit o$f$ the quotient o$f$ two functions is the quotient of their limits if the limit in the denominator is not equal to 0. – 2012-10-25
1 Answers
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You might want to check if this result is true. Since $g(t)=1/t$ is continuous a.e., $g(X_{n})$ converges to $g(X)$ a.s.