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ON MARCINKIEWICZ'S TYPE LAW FOR FUZZY RANDOM SETS
ON MARCINKIEWICZ'S TYPE LAW FOR FUZZY RANDOM SETS
Journal of applied mathematics & informatics. 2014. Jan, 32(1_2): 55-60
  • Received : July 03, 2013
  • Published : January 30, 2014
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Kwon, Joong-Sung
Shim, Hong-Tae

Abstract
In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n
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