My probability professor proved the property of "continuity to the right" of the repartition fucntion F by showing that F(x+1/n)--->F(x). But as I remember it, continuity to the right means that for(adsbygoogle = window.adsbygoogle || []).push({}); anysequence {a_n} of elements of (x,+infty) that converges to x, F(a_n) converges to F(x). Is there some subtlety I'm not aware of by which showing F(x+1/n)--->F(x) is sufficient to show it works for any sequence?

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# Continuity to the right.

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