Daniell-Greco-Stone representation type theorem for autocontinuous from above functionals.
Economic and management theories are very often based in their applications on the perception of homogeneity of the application space. The purpose of this article is to query such a conviction and indicate new possible directions of discipline development. The article deals with symbiosis of process and his steering model as a process of management. It is possible that in relative near future it will be necessary to accept approaches and changes in interpretations of decision-making. Applications...
Let be an additive function on a ring of sets, with values in a commutative Hausdorff topological group, and let be an ideal of . Conditions are given under which can be represented as the sum of two additive functions, one essentially supported on , the other vanishing on . The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.
We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.
We show that if ℱ is a hereditary family of subsets of satisfying certain definable conditions, then the reals are precisely the reals α such that . This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the -encodable reals is also shown.