Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space

Details Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space

2011-07-24

arxiv.org/abs/1107.4726v2

Mathematics

Functional Analysis

26 pages

Scientific paper

Motivated by the recent work on conditional risk measures, this paper studies the Ekeland's variational principle for a proper, lower semicontinuous and lower bounded $\bar{L}^{0}-$valued function, where $\bar{L}^{0}$ is the set of equivalence classes of extended real-valued random variables on a probability space. First, we prove a general form of Ekeland's variational principle for such a function defined on a complete random metric space. Then, we give a more precise form of Ekeland's variational principle for such a local function on a complete random normed module. Finally, as applications, we establish the Bishop-Phelps theorem in a complete random normed module under the framework of random conjugate spaces.

Affiliated with

Also associated with

No associations

Rating

Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-76449