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The law of large numbers with exceptional sets

✍ Scribed by István Berkes

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
102 KB
Volume
55
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 su cient criteria for the validity of such laws.

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Weak laws of large numbers for fuzzy ran
Weak laws of large numbers for fuzzy random sets
✍ Robert L. Taylor; Lynne Seymour; Yinpu Chen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 472 KB

Weak laws of large numbers are obtained for fuzzy random sets in separable Banach spaces. These results are obtained under varying hypotheses of independence, exchangeability and tightness conditions on the distributions.