Decision Theory Based on Non-Additive Measures
Decision-making for long memory data in technical-economic design, fractals and decision area bubbles
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...
Decision-making under uncertainty processed by lattice-valued possibilistic measures
The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.
Decomposable sets and Musielak-Orlicz spaces of multifunctions
We introduce the Musielak-Orlicz space of multifunctions and the set of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space and the set .
Décomposition des mesures selon la dimension
Décomposition et classification des systèmes dynamiques
Decomposition in the product of a measure space and a Polish space
Decomposition of group-valued additive set functions
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.
Decomposition of group-valued measures on orthoalgebras
We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the case where the measure is order bounded instead of being positive. This last result generalizes A. D. Aleksandrov's...
Decomposition of -group-valued measures
We deal with decomposition theorems for modular measures defined on a D-lattice with values in a Dedekind complete -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for -group-valued...
Decomposition of set functions with values in a topological semigroups
Decomposition theorems in measure theory
Decompositions of set functions
Dedekind extension of measures with values in vector lattices.
Definability of small puncture sets
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.
Definable hereditary families in the projective hierarchy
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.
Définition axiomatique de la mesure de Hausdorff
Dense sums
Denseness and Borel complexity of some sets of vector measures
Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets and of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...
Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy
Let Tbe a measurable transformation of a probability space , preserving the measureπ. Let X be a random variable with law π. Call K(⋅, ⋅) a regular version of the conditional law of X given T(X). Fix . We first prove that ifB is reachable from π-almost every point for a Markov chain of kernel K, then the T-orbit of π-almost every point X visits B. We then apply this result to the Lévy transform, which transforms the Brownian motion W into the Brownian motion |W| − L, where L is the local time...