The affine representation theorem for abstract convex geometries

The affine representation theorem for abstract convex geometries

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Choice functions and abstract convex geometries *

A main aim of this paper is to make connections between two well – but up to now independently – developed theories, the theory of choice functions and the theory of closure operators. It is shown that the classes of ordinally rationalizable and path independent choice functions are related to the classes of distributive and anti-exchange closures.  1999 Elsevier Science B.V. All rights reserved.

Representation theorem for convex effect algebras

Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation ...

Representation Theorem for Convex Nonparametric Least Squares

We examine a nonparametric least squares regression model where the regression function is endogenously selected from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions is perfectly represented by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrain...

A Representation Theorem for Bounded Convex Sets