A uniform strong law of large numbers for partial sum processes of Banach space-valued random sets

1998 ◽  
Vol 38 (1) ◽  
pp. 21-25
Author(s):  
Lee-Chae Jang ◽  
Joong-Sung Kwon
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Random Sets ◽  
Strong Law ◽  
Partial Sum ◽  
Large Numbers

scholarly journals Strong Law of Large Numbers for Banach Space Valued Random Sets

1983 ◽  
Vol 11 (1) ◽  
pp. 222-224 ◽  
Author(s):  
Madan L. Puri ◽  
Dan A. Ralescu
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Random Sets ◽  
Strong Law ◽  
Large Numbers

scholarly journals A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
R. Ghasemi ◽  
A. Nezakati ◽  
M. R. Rabiei
Keyword(s):  
Metric Space ◽  
Convex Sets ◽  
Law Of Large Numbers ◽  
Compact Convex ◽  
Random Sets ◽  
Fuzzy Metric Space ◽  
Strong Law ◽  
Fuzzy Metric ◽  
Large Numbers ◽  
Fuzzy Random

The main purpose of this paper is to consider the strong law of large numbers for random sets in fuzzy metric space. Since many years ago, limited theorems have been expressed and proved for fuzzy random variables, but despite the uncertainty in fuzzy discussions, the nonfuzzy metric space has been used. Given that the fuzzy random variable is defined on the basis of random sets, in this paper, we generalize the strong law of large numbers for random sets in the fuzzy metric space. The embedded theorem for compact convex sets in the fuzzy normed space is the most important tool to prove this generalization. Also, as a result and by application, we use the strong law of large numbers for random sets in the fuzzy metric space for the bootstrap mean.

Sample Behavior and Laws of Large Numbers for Gaussian Random Elements

2003 ◽  
Vol 10 (4) ◽  
pp. 637-676
Author(s):  
Z. Ergemlidze ◽  
A. Shangua ◽  
V. Tarieladze
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

Abstract Criteria for almost sure boundedness and convergence to zero almost surely of Banach space valued independent Gaussian random elements are found. The obtained statements can be viewed as vector-valued versions of the corresponding results due to N. Vakhania. Moreover, from the obtained statements a strong law of large numbers is derived in the form of Yu. V. Prokhorov.

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