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Results tagged with growth-rate
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user 33741
6
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Functions with at most linear growth at infinity: is the constant itself continuous?
The answer is no to both your hopes: it can happen that neither $M_{f_n}\to M_f$ nor $\sup_n M_{f_n}<+\infty$ hold, although $M_f<\infty$.
As a counter-example take
$$
f_n(x)=\max(0,n(x-n)).
$$
(I'm t …
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