The purpose of this note is to provide some clarification on the so-called representation theorems of neoclassical utility theory. In particular, it is argued that there is some misunderstanding regarding precisely what conclusions may be properly drawn from these theorems, and that there seems to be a tendency among neoclassical economists to misapply these theorems. Reference will be made to ...

We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity and time reversal symmetry. collect transformation properties related to these Fock space representation as well Schr\"odinger representation. As an application, we generalize improve theorems about Kramer's degeneracy electrodynamics.

A discussion of the convergence of approximating functions for a given function of two variables ƒ(#, y), just as in the case of functions of one variable, can be based on two sets of theorems: (1) theorems on the existence of functions of closest approximation; (2) theorems on the representation of ƒ(#, y) by means of finite sums constructed in a specific way. From the first group we shall mak...

We claim that mathematical databases should be more than a collection of domains with associated theorems; in particular theorems should be stated as general as possible, that is independent of domains. A database then should be able to check whether such a general theorem holds in a particular domain. To this end we use a properties-based representation for both theorems and domains, and prese...

The objective of this paper is to provide continuous utility representation theorems analogous to Debreu’s classic utility representation theorem, albeit for preference relations that may fail to be complete and/or transitive. Specifically, we show that every (continuous and) reflexive binary relation on a (compact) metric space can be represented by means of the maxmin, or dually, minmax, of a...

We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Represent...