Banach Space And Fuzzy Random Variables, Strong Law Of Large Numbers

This thesis is finished under the guidance of professor Zhang Lixin,during my master of science.It consists of two chapters.Strong laws of large numbers(SLLN) play very important roles in research of prob-ability.In this thesis,we show SLLN in general Banach space or convex,compact and bounded fuzzy random variables.Chapter 1 Chung-Teicher type SLLN in general Banach spaceIn this chapter,we show that Chung-Teicher type conditions for SLLN under the assumption that the weak laws of large numbers holds.This chapter extends the work of A.Kuczmaszewska and D.Szynal[21].We get more abroad and more common results.Theorem 1.2:Let {X_n, n ≥ 1} be a sequence of independent B-valued random el-ements,sequence {a_n, n ≥ 1} and sequence {b_n, n≥ 1} be positive constant sequences such that 0 < b_n ↑ ∞;φ(x) satisfies φ : R~+ â†' R~+, (?) φ(x) = ∞,φ(x) ↑,andCase(a) φ(x)/(x~t)↓ , t ≥ 1:Case(b) φ(x)/(x~t) ↑, φ(x)/(x~t+p-1)↓, t≥1,1 l}be a sequence of independentFc6oc(i?")-valued fuzzy random variables and {an, n > l}a sequence of constants such that 0 < an | oo,0.Assume that< oo,rs=l z=lsome s > 0,then the following are equivalentwhereC is complete convergence^ is fuzzy set.if x ^ O,then 0(x) = 0;if x — O,then 0(x) = 1.