  Limit theorems for non-additive probabilities or non-linear expectations are
challenging issues which have raised progressive interest recently. The purpose
of this paper is to study the strong law of large numbers and the law of the
iterated logarithm for a sequence of random variables in a sub-linear
expectation space under a concept of extended independence which is much weaker
and easier to verify than the independence proposed by Peng (2008b). We
introduce a concept of extended negative dependence which is an extension of
this kind of weak independence and the extended negative independence relative
to classical probability appeared in recent literatures. Powerful tools as the
moment inequality and Kolmogorov's exponential inequality are established for
this kind of extended negatively independent random variables, which improve
those of Chen, Chen and Ng(2010) a lot. And the strong law of large numbers and
the law of iterated logarithm are obtained by applying these inequalities.
