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Easure and Integration in the Alternative set Theory

Miodrag Rašković (1981)

Publications de l'Institut Mathématique

Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem

M. Laczkovich (1990)

Journal für die reine und angewandte Mathematik

Equidecomposability of Jordan domains under groups of isometries

M. Laczkovich (2003)

Fundamenta Mathematicae

Let $G_{d}$ denote the isometry group of $ℝ^{d}$ . We prove that if G is a paradoxical subgroup of $G_{d}$ then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system $ℱ_{d}$ of Jordan domains with differentiable boundaries and of the same volume such that $ℱ_{d}$ has the cardinality of the continuum, and for every amenable subgroup G of $G_{d}$ , the elements of $ℱ_{d}$ are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...

Equipartitioning Common Domains of Non-Atomic Measures.

Theodore P. Hill (1985)

Mathematische Zeitschrift

Equivalence et orthogonalité des mesures aléatoires engendrées par martingales positives homogènes

Ai Fan (1991)

Studia Mathematica

Extensión de medidas difusas usando la esperanza monótona.

Manuel Jorge Bolaños Carmona, María Teresa Lamata Jiménez, Serafín Moral Callejón (1987)

Stochastica

The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...