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Random normed linear structures. (English) Zbl 0868.46059
Summary: This paper shows that any random normed linear space is a metrizable topological linear space. A compatible translation invariant metric is constructed.

##### MSC:
 46S50 Functional analysis in probabilistic metric linear spaces 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 47H10 Fixed-point theorems 47S50 Operator theory in probabilistic metric linear spaces 54E70 Probabilistic metric spaces