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Decision-making under uncertainty processed by lattice-valued possibilistic measures

Ivan Kramosil (2006)

Kybernetika

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

Andrzej Kasperski (2005)

Banach Center Publications

We introduce the Musielak-Orlicz space of multifunctions X m , φ and the set S F φ of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to X m , φ . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space X m , φ and the set S F φ .

Decomposition of group-valued additive set functions

Tim Traynor (1972)

Annales de l'institut Fourier

Let m be an additive function on a ring H of sets, with values in a commutative Hausdorff topological group, and let K be an ideal of H . Conditions are given under which m can be represented as the sum of two additive functions, one essentially supported on K , the other vanishing on K . 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

Paolo De Lucia, Pedro Morales (1998)

Fundamenta Mathematicae

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 ℓ -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

We deal with decomposition theorems for modular measures μ : L → G defined on a D-lattice with values in a Dedekind complete ℓ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete ℓ -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 ℓ -group-valued...

Definability of small puncture sets

Andrés Eduardo Caicedo, John Daniel Clemens, Clinton Taylor Conley, Benjamin David Miller (2011)

Fundamenta Mathematicae

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

R. Barua, V. Srivatsa (1992)

Fundamenta Mathematicae

We show that if ℱ is a hereditary family of subsets of ω ω satisfying certain definable conditions, then the Δ 1 1 reals are precisely the reals α such that β : α ∈ Δ 1 1 ( β ) ∉ ∈ ℱ . 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 Q 2 n + 1 -encodable reals is also shown.

Dense sums

G. Fano, G. Gallavotti (1972)

Annales de l'I.H.P. Physique théorique

Denseness and Borel complexity of some sets of vector measures

Zbigniew Lipecki (2004)

Studia Mathematica

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 ν ( X ) and ν ( X ) 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

Jean Brossard, Christophe Leuridan (2012)

Annales de l'I.H.P. Probabilités et statistiques

Let Tbe a measurable transformation of a probability space ( E , ℰ , π ) , 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 B ∈ ℰ . 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...

Density covers

A. M. Bruckner, Charles L. Thorne (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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