Metric function spaces and reflected spaces
In this paper we first define what is meant by the term metric function space. Basically, a metric function space consists of a set of functions F and a metric p on F which satisfies certain axioms. For example, the Lp spaces and the L(p, q) spaces are metric function spaces. For certain metric function spaces we can form what we will call the reflected space. Theorem 12 states that the reflected space to a metric function space is itself a metric function space. Theorem 13 shows that the reflected space to the reflected space of a metric function space is the original space. Theorem 14 gives a relation between a metric function space and its reflected space, namely, that a metric function space is absolutely continuous if and only if its reflected space has the truncation property.
Gerber, Brian Paul. "Metric function spaces and reflected spaces." (1969) Master’s Thesis, Rice University. https://hdl.handle.net/1911/90087.