Random convex analysis (II): Continuity and subdifferentiability theorems in <italic>L</italic>⁰-pre-barreled random locally convex modules

DOI10.1360/N012015-00042zbMath1488.46111arXiv1503.08637OpenAlexW3103667985MaRDI QIDQ5018040

Shien Zhao, Tie-Xin Guo, Xiao Lin Zeng

Publication date: 17 December 2021

Published in: SCIENTIA SINICA Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.08637

zbMATH Keywords

continuitylocally \(L^0\)-convex topologyrandom locally convex modulesubdifferentiabilityrandom conjugate spaces

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Barrelled spaces, bornological spaces (46A08) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Derivatives of functions in infinite-dimensional spaces (46G05) Topological linear spaces and related structures (46A99)

Related Items (8)

\(L^0\)-convex compactness and random normal structure in \(L^0(\mathcal{F}, B)\) ⋮ On \(L^0\)-convex compactness in random locally convex modules ⋮ Stability in locally \(L^{0}\)-convex modules and a conditional version of James' compactness theorem ⋮ A characterization for a complete random normed module to be mean ergodic ⋮ Some results on random smoothness ⋮ Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations ⋮ L⁰-convex compactness and its applications to random convex optimization and random variational inequalities ⋮ Semigroups of continuous module homomorphisms on complex complete random normed modules

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