(1) Air Force Institute of Engineering, 710038 Xi’an, China
Abstract:
The fourth axiom in the definition of real random normed module is superfluous. A necesmry and sufficient condition is given
that continuous random linear functionals over complex random normed spaces are a. s. bounded, and furthermore, in the sense
of inometrical isomorphism it is proved the fourth axiom in the complex random normed module is superfluous.