We generalise the Riesz representation theorems for positive linear functionals on $$\text {C}_{\text {c}}(X)$$ and {0}}(X)$$ , where X is a locally compact Hausdorff space, to operators from these spaces into partially ordered vector space E. The representing measures are defined Borel $$\sigma $$ -algebra of take their values in extended cone corresponding integrals order integrals. give expl...

The relationship between theorems and lemmas in mathematical reasoning is often vague. No system exists that formalizes the structure of theorems in a mathematical library. Nevertheless, the decisions we make in creating lemmas provide an inherent hierarchical structure to the statements we prove. In this paper, we develop a formal system that organizes theorems based on scope. Lemmas are simpl...

Representation theorems are established for fixed points of adjoint functors between categories enriched in a small quantaloid. In a very general setting these results set up a common framework for representation theorems of concept lattices in formal concept analysis (FCA) and rough set theory (RST), which not only extend the realm of formal contexts to multi-typed and multi-valued ones, but a...