Abstract
This chapter explains the concept of log-convex sets of random variables. It presents an assumption where if F is a nonempty set of random variables that are defined on the same probability space, then each random variable in F would become finite expectation. A set F can arise naturally, for example, in the context of a type of constrained extremum problem of information theory. However, in such a context it is uncertain whether F satisfies the property that there exists a unique random variable. The chapter presents a theorem where F is a nonempty set of random variables defined on the same probability space, each of which has finite expectation. If F is log-convex and that B(F) > -∞. Then, up to almost sure equivalence, there is a unique Y* in the L1 closure of F such that EY* = B(F).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
