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I know this:

If (a_n) is a bounded below decreasing sequence, then

lim (a_n) = inf { a_n / n = 1,... }

n->oo

How to translate this to real functions ?

I mean, I have read that:

lim (sup { f(x) / 0< |x-a|< e}) =

e->0

inf { sup {f(x) / 0< |x-a|< e} / e > 0}

and i suppose it has something to do with the previous but I fail to see how.

Can you help me?

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# From decreasing sequences to decreasing functions

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