  This paper introduces the notion of pseudo-independence on the sublinear
expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical
conditional expectation, and the relations between pseudo-independence and
Peng's independence are detailed discussed. Law of large numbers and central
limit theorem for pseudo-independent random variables are obtained, and a
purely probabilistic proof of Peng's law of large numbers is also given. In the
end, some relevant counterexamples are indicated that Peng's law of large
numbers and central limit theorem are invalid only with the first and second
moment conditions respectively.

Probability