On Random Uniform Convexity

The paper is devoted to a further discussion about the notion of random uniform convexity.First,we point out that modulus of random convexity is well defined for an arbitrary random normed module via a special stratification partition.Consequently,many known results in recent literature are improved.Then a new property closely related to random uniform convexity is proposed and studied,which elucidates the complication of random uniform convexity from a new angle.