Preference, topology and measure

A symmetric difference metric topology on the collection of binary relations on a countably infinite set provides a new setting for the study of properties of preferences and, as an illustration, is used to lend credence and meaning to some simple intuitions about properties of binary relations. A finite measure on a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">σ</mi> </math> </EquationSource> </InlineEquation>-algebra over the same collection of binary relations is used to provide support for the topological results. Copyright Springer-Verlag Berlin Heidelberg 2014