Some results on random smoothness

Abstract

Abstract Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for random norms, and its relation to random smoothness is given. The results are helpful in the further study of geometry of random normed modules.

Keywords

• random normed module
• random strict convexity
• random smoothness
• Gâteaux differentiability