O'Neil, Richard2016-04-222016-04-221969Gerber, Brian Paul. "Metric function spaces and reflected spaces." (1969) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/90087">https://hdl.handle.net/1911/90087</a>.https://hdl.handle.net/1911/90087In 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.23 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE1123reformatted digitalThesis Math. 1969 Gerber