By Barry Max Brandenberger
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Extra info for Encyclopedia of Mathematics Da-Lo
It should be noted that A > 0, convex, and not symmetric, which is reflected by (similar) properties of A. , in Rao and Ren [(2002), Chapter VIII]. The point to note is the fundamental role played by the complementary function A for the assertion of (12). Let us abstract this conclusion to proceed further. Motivated by the special Bernoulli problem, one may term Qn(-) the 'large deviation probability' and (12) implies that it decreases to zero exponentially fast when A does not contain E(Xi), the pointwise limit of the Yn being a consequence of the Kolmogorov law of large numbers.
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