Article 35: Prevention of Abduction, Sale, and Trafficking

Abstract‘There should be strong laws against child abduction and trafficking made by the government to protect the interest of children.’ (Africa).

The Strong Law of Large Numbers

This chapter focuses largely on methods of proof of the strong law, building on the fundamental convergence lemma. It covers Kolmogorov's three‐series theorem, strong laws for martingales, and random weighting. Then a range of strong laws are proved for mixingales and for near‐epoch dependent and mixing processes.

The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.

On the strong law of large numbers for ϕ-sub-Gaussian random variables

UDC 517.9 For let if and if . For a random variable ξ let denote ; is a norm in a space - subgaussian random variables. We prove that if for a sequence there exist positive constants and such that for every natural number the following inequality holds then converges almost surely to zero as . This result is a generalization of the strong law of large numbers for independent sub-Gaussian random variables [see R. L. Taylor, T.-C. Hu, <em>Sub-Gaussian techniques in proving strong laws of large numbers</em>, Amer. Math. Monthly, <strong>94</strong>, 295 – 299 (1987)] to the case of dependent -sub-Gaussian random variables.