The law of large numbers with exceptional sets
We investigate the law of large numbers with exceptional n-sets, i.e. when the theorem is required to hold only for almost all n, in the sense of a suitable measure on the integers. We prove the surprising result that in the presence of such exceptional sets, the weak and strong laws of large numbers become equivalent. We also give necessary and sufficient criteria for the validity of such laws.
Volume (Year): 55 (2001)
Issue (Month): 4 (December)
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