scholarly journals The tau-additive measure and its connection with the lambda-additive measure

2021 ◽  
Author(s):  
Tamás Jónás ◽  
Hassan S. Bakouch ◽  
József Dombi
Keyword(s):  
Additive Measure

scholarly journals Wirtinger integral inequalities for pseudo-integrals and pseudo-additive measure

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Guo ◽  
Xianjun Zhu
Keyword(s):  
Continuous Function ◽  
Integral Inequalities ◽  
Additive Measure ◽  
The Real ◽  
First Case ◽  
Interval Valued

AbstractThe main purpose of this paper is to show Wirtinger type inequalities for the pseudo-integral. We are concerned with pseudo-integrals based on the following three canonical cases: in the first case, the real semiring with pseudo-operation is generated by a strictly monotone continuous function g; in the second case, the pseudo-operations include a pseudo-multiplication and a power arithmetic addition; in the last case, ⊕-measures are interval-valued. Examples are given to illustrate these equalities.

Additive entropy requires additive measure

1978 ◽  
Vol 30 (1) ◽  
pp. 293-296
Author(s):  
G�nther Palm
Keyword(s):  
Additive Measure

scholarly journals Separability of the L1-space of a vector measure

1992 ◽  
Vol 34 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Metric Space ◽  
Classical Result ◽  
Vector Measure ◽  
Symmetric Difference ◽  
Outer Measure ◽  
Additive Measure ◽  
Image Position

Let Σ be a σ-algebra of subsets of some set Ω and let μ:Σ→[0,∞] be a σ-additive measure. If Σ(μ) denotes the set of all elements of Σ with finite μ-measure (where sets equal μ-a.e. are identified in the usual way), then a metric d can be defined in Σ(μ) by the formulahere E ΔF = (E\F) ∪ (F\E) denotes the symmetric difference of E and F. The measure μ is called separable whenever the metric space (Σ(μ), d) is separable. It is a classical result that μ is separable if and only if the Banach space L1(μ), is separable [8, p.137]. To exhibit non-separable measures is not a problem; see [8, p. 70], for example. If Σ happens to be the σ-algebra of μ-measurable sets constructed (via outer-measure μ*) by extending μ defined originally on merely a semi-ring of sets Γ ⊆ Σ, then it is also classical that the countability of Γ guarantees the separability of μ and hence, also of L1(μ), [8, p. 69].

scholarly journals THE INTERVAL-VALUED INTUITIONISTIC FUZZY GEOMETRIC CHOQUET AGGREGATION OPERATOR BASED ON THE GENERALIZED BANZHAF INDEX AND 2-ADDITIVE MEASURE

2015 ◽  
Vol 21 (2) ◽  
pp. 186-215 ◽  
Author(s):  
Fanyong MENG ◽  
Qiang ZHANG ◽  
Jiaquan ZHAN
Keyword(s):  
Geometric Mean ◽  
Fuzzy Measure ◽  
Entropy Measure ◽  
Additive Measure ◽  
Banzhaf Index ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Additive Measures ◽  
Interval Valued

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively.

A Remark on Disintegrations With Almost All Components Non -Additive

1979 ◽  
Vol 31 (4) ◽  
pp. 786-788 ◽  
Author(s):  
Nghiem Dang-Ngoc
Keyword(s):  
Real Function ◽  
Measure Space ◽  
Gibbs States ◽  
List Type ◽  
Additive Measure ◽  
Finitely Additive Measure ◽  
Coin Tossing ◽  
Definition Of ◽  
Almost All

We extend a theorem of L. E. Dubins on “purely finitely additive disintegrations” of measures (cf. [4]) and apply this result to the disintegrations of extremal Gibbs states with respect to the asymptotic algebra enlarging another result of L. E. Dubins on the symmetric coin tossing game.We recall the following definition of L. E. Dubins (cf. [3], [4]): Let (X , , μ) be a measure space, a sub σ-algebra of . A real function σx (A), is called a measurable-disintegration of μ if:(i) ∀x ∊ X , σx(.) is a finitely additive measure .(ii) ∀A ∊ , σ. (A) is constant on each -atom.(iii) For each A ∊ , σ. (A) is measurable with respect to the completion of by μ and (iv)σx(B) = 1 if x ∊ B ∊ .

A Banach Space in Which a Ball is Contained in the Range of Some Countably Additive Measure is Superreflexive

1990 ◽  
Vol 33 (1) ◽  
pp. 45-49 ◽  
Author(s):  
Yeneng Sun
Keyword(s):  
Banach Space ◽  
Additive Measure ◽  
General Method

AbstractA nonstandard proof of the fact that a Banach space in which a ball is contained in the range of a countably additive measure is superreflexive is given. The proof is an application of a general method in which we first transfer certain standard objects to the nonstandard hull of a Banach space and then, using the quite well developed theory of nonstandard hulls, derive results about the objects in the original Banach space. It also provides us with an example of the applications of the theory of nonstandard hull valued measures.

scholarly journals When is the algebra of regular sets for a finitely additive borel measure a α-algebra?

1982 ◽  
Vol 33 (3) ◽  
pp. 374-385 ◽  
Author(s):  
Thomas E. Armstrong
Keyword(s):  
Borel Measure ◽  
Convex Set ◽  
Additive Measure ◽  
Dimensional Simplex ◽  
Finitely Additive Measure ◽  
Regular Algebra ◽  
Finite Dimensional ◽  
Regular Sets ◽  
Dirac Measures

AbstractIt is shown that hte algebra of regular sets for a finitely additive Borel measure μ on a compact Hausdroff space is a σ-algebra only if it includes the Baire algebra and μ is countably additive onthe σ-algebra of regular sets. Any infinite compact Hausdroff space admits a finitely additive Borel measure whose algebra of regular sets is not a σ-algebra. Although a finitely additive measure with a σ-algebra of regular sets is countably additive on the Baire σ-algebra there are examples of finitely additive extensions of countably additive Baire measures whose regular algebra is not a σ-algebra. We examine the particular case of extensions of Dirac measures. In this context it is shown that all extensions of a {0, 1}-valued countably additive measure from a σ-algebra to a larger σ-algebra are countably additive if and only if the convex set of these extensions is a finite dimensional simplex.

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