Search results for "Representation theorem"
showing 10 items of 32 documents
A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions
2009
We proved in our earlier paper [9] that in case of separable Banach space-valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selectors and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Applying the representation theorem we describe the multipliers of the Henstock-Kurzweil-Pettis integrable multifunctions. Then we use this description to obtain a characterization of the Henstock-Kurzweil-Pettis integrability in terms of subadditive operators.
The Riesz Representation Theorem and Extension of Vector Valued Additive Measures
2001
A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms
1983
All known connectives 'and'/'or' for fuzzy sets or some classes can be introduced as t-norms/t-conorms, where Ling's representation theorem is used as a basic tool, and which is illustrated by various known and new examples (Section 2). Given a strict negation function and one connective, the other can be constructed, so that the corresponding De Morgan law is valid. In case of given Archimedean connectives, there can be constructed negation functions (Section 3). Given a non-strict Archimedean connective, a negation function and the other connective can be constructed, so that in addition to the De Morgan laws, the excluded middle law and the law of non-contradiction are valid, i.e. the ne…
Quadratic variation of martingales in Riesz spaces
2014
We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)
On a representation theorem for finitely exchangeable random vectors
2016
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$. We give an alternative and shorter proof of the representation result (Jaynes \cite{Jay86} and Kerns and Sz\'ekely \cite{KS06}) stating that the law of $X$ is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite $S$. The passing from finite $S$ to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our p…
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
2015
The theory of HenstockâKurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.
Unbounded Linear Operators in Hilbert Spaces
2002
In order to make this monograph self-contained, we summarize in this chapter some basic definitions and results for unbounded linear operators in a Hilbert space. In Section 1.1, we recall the definitions of C*-algebras and von Neumann algebras. In Section 1.2, we define and investigate the notion of closedness, the closure and the adjoint of an unbounded linear operator in a Hilbert space. Section 1.3 is devoted to the Cayley transform approach to the self-adjointness of a symmetric operator. Section 1.4 deals with the self-adjoint extendability of a symmetric operator with help of the deficiency spaces. In Section 1.5, we extend to unbounded self-adjoint operators the spectral theorem and…
Transport equations and quasi-invariant flows on the Wiener space
2010
Abstract We shall investigate on vector fields of low regularity on the Wiener space, with divergence having low exponential integrability. We prove that the vector field generates a flow of quasi-invariant measurable maps with density belonging to the space L log L . An explicit expression for the density is also given.
Equivalence Relations on Stonian Spaces
1996
Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.