Spitzer's Strong Law of Large Numbers in Nonseparable Banach Spaces

Berthold Wittje ()

Journal of Theoretical Probability, 2000, vol. 13, issue 1, 85-92

Abstract: Abstract It is well known, that for the sums of i.i.d. random variables we have S n/n → 0 a.s. iff ∑∞ n=1 1/nP(|S n| > nε) 0 (Spitzer's SLLN). The result is also known in separable Banach spaces. It will be shown, that this also holds in nonseparable (= not necessarily separable) Banach spaces without any measurability assumption. In the theory of empirical processes this gives a characterization of Glivenko-Cantelli classes.

Keywords: strong law of large numbers; Glivenko–Cantelli class; nonmeasurable function (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007730809136

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