# Advances in Mathematical Economics

Volume 19

## Dublin Core

### Title

Advances in Mathematical Economics

Volume 19

Volume 19

### Subject

Advances in Mathematical Economics

Volume 19

Volume 19

### Description

We study the integration of fuzzy level sets associated with a fuzzy

random variable when the underlying space is a separable Banach space or a

weak star dual of a separable Banach space. In particular, the expectation and the

conditional expectation of fuzzy level sets in this setting are presented. We prove

the SLLN for pairwise independent identically distributed fuzzy convex compact

valued level sets through the SLLN for pairwise independent identically distributed

convex compact valued random set in separable Banach space. Some convergence

results for a class of integrand martingale are also presented.

random variable when the underlying space is a separable Banach space or a

weak star dual of a separable Banach space. In particular, the expectation and the

conditional expectation of fuzzy level sets in this setting are presented. We prove

the SLLN for pairwise independent identically distributed fuzzy convex compact

valued level sets through the SLLN for pairwise independent identically distributed

convex compact valued random set in separable Banach space. Some convergence

results for a class of integrand martingale are also presented.

### Creator

Shigeo Kusuoka

Toru Maruyama

Toru Maruyama

### Files

### Collection

### Citation

Shigeo Kusuoka
Toru Maruyama, “Advances in Mathematical Economics
Volume 19,”

*Portal Ebook UNTAG SURABAYA*, accessed July 21, 2024, https://ebook.untag-sby.ac.id/items/show/40.