Integral with respect to a pre-measure
Integrale monotono
Integration by Parts
Intégration dans les semi-groupes
Integration of real functions with respect to a -measure
Integration on generalized measure spaces
Integration with respect to orthogonally scattered measures
Integratioonstheorie und quasinormierte Gruppen.
Limites et fonctions d'ensemble
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Lower semicontinuity of multiple -quasiconvex integrals
Lower semicontinuity results are obtained for multiple integrals of the kind , where is a given positive measure on , and the vector-valued function belongs to the Sobolev space associated with . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to . More precisely, for fully general , a notion of quasiconvexity for along the tangent bundle to , turns out to be necessary for lower...
Lower semicontinuity of multiple µ-quasiconvex integrals
Lower semicontinuity results are obtained for multiple integrals of the kind , where μ is a given positive measure on , and the vector-valued function u belongs to the Sobolev space associated with μ. The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to μ. More precisely, for fully general μ, a notion of quasiconvexity for f along the tangent bundle to μ, turns out to be necessary for lower...
Mazur spaces.
Mengenwertige Masse und Fortsetzungen.
Möbius fitting aggregation operators
Standard Möbius transform evaluation formula for the Choquet integral is associated with the -aggregation. However, several other aggregation operators replacing operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...
Multidimensional extension of L. C. Young's inequality.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication, distributivity and fuzzy-integral. II
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...
Multiplication, distributivity and fuzzy-integral. III
Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.
Nonlinear integrals