Functions determining locally solid topological Riesz spaces continuously embedded in $L^0$

Abstract

We present a class of non-negative functions, acting on a solid vector subspace $X$ of $L^0$, enjoying the following property: each member of the class determines on $X$ a locally solid topological Riesz space structure which is continuously embedded into $L^0$. These functions are neither necessarily monotone, nor subadditive. Special instances are provided by function norms and quasi-norms on $X$.