A remark on the asymptotic tightness in ${\ell }^{\infty }([a,b])$

Abstract

In this note, we extend a simple criteria for uniform tightness in $C(0,1)$, the class of real continuous functions defined on $(0,1)$, given in Theorem 8.3 of Billingsley to the asymptotic tightness in ${\ell }^{+\infty }([a,b])$, the class of real bounded functions defined on $[a,b]$ with $a<b$, in the lines of Theorems 1.5.6 and 1.5.7 in van der vaart and Wellner.

4 pages

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