1,720,982 research outputs found
Convergence theorems for measures with values in Riesz spaces
No full textA survey of convergence results for l-group-valued measures is given, e.g. Vitali-Hahn-Saks and Diedonne' theorems: in particular properties of uniform additivity are stressed, under pointwise convergence, and also decomposition theorems have been discussed in order to obtain convergence of the Lebesgue decompositions
Multidimensional variations and countably additive restrictions
No full textThe main convergence theorems in probability theory are discussed and stated in the finitely additive case. Motivations for this are given, and technical methods are described, based upon properties of functions having bounded variation, in order to prove that, under mild assumptions, the Central Limit Theorem and the Laws of Large Numbers essentially hold also in this case
Sull'approssimazione dell'integrale di Burkill-Cesari di funzionali sublineari su misure ed applicazioni all'integrale multiplo del calcolo delle variazioni
No full textWe study and discuss some approximation formulae for the Serrin Integral of Calculus of Variations. They are formulated in such a way that we can subsequently apply them to some situations of convergence in area in two dimensional frames
Su alcuni problemi relativi a misure scalari subadditive e applicazioni al caso dell' additività finita
No full textGiven a set X and a semiconvex subadditive measure on it, we establish topological properties of the power set of X, in particular arcwise connectedness, that allow us to investigate the range of signed finitely additive measures (charges), which are strongly non atomic (or equivalently, strongly bounded). In particular we provide the following extension of the Lyapounov Theorem in the signed case: the range of such a finitely additive measure is always convex. On the contrary we provide an example of a charge having non closed range. We also give a partial answer to the question relative to the existence of countably additive restrictions of a charge
Differential Calculus in Riesz spaces and applications to g-calculus
No full textWe study and develop several features of the theory of Differential and Integral Calculus in Riesz spaces, and we apply them to investigate some properties of the g-calculus in this setting and to solve different types of functional, stochastic and differential equations
Teoremi di approssimazione per l'integrale multiplo del calcolo delle variazioni
No full textwe state some approximation theorems for the multiple integral of Calculus of Variations. These theorems are formulated in a very general setting, which includes and unifies some classical results on the area of a surface reached by C.Vint
Dieudonnè-type theorems for set functions with values in (l)-groups
No full textSome versions of Dieudonne' theorems are given for finitely additive set functions, not necessarily positive, taking values in Dedekind-complete (l)-groups. In our setting, regularity, strong boundedness and pointwise convergence of the measures involved are intended in the setting of (D)-convergence and with respect of a same regulator
Alcune limitazioni per l'integrale di Riemann-Stieltjes e per l'integrale di Weierstrass
No full textRecently there have appeared several works establishing estimates for Riemann-Stieltjes (R-S) integrals. We mention only those of R. Darst and H. Pollard [Proc. Amer. Math. Soc. 25 (1970), 912--913] and of P. R. Beesack [Rocky Mountain J. Math. 5 (1975), 75-78] and refer the reader to the bibliographies therein for further information. Darst and Pollard [op. cit.] studied the integral under classical hypotheses. Their results were generalized by Beesack [op. cit.], who, among other things, established upper and lower bounds for the classical integral as well as for improper integrals. In this paper we attack the problem of determining inequalities for R-S integrals using a generalized variation. In Section 1 we recall the definition of generalized variation and some properties related to it. In Section 2 we discuss briefly the theorems of T. H. Hildebrandt [Introduction to the theory of integration, Academic Press, New York, 1963] related to the R-S integral and we present some further results including a new necessary condition for the existence of this integral. Finally, in Section 3 we determine various estimates for R-S integrals and compare them with one another and with those of Beesack [op. cit.]. Finbally we generalize one estimate to the Weierstrass integral
Some new results about Brooks-Jewett and Dieudonné-type theorems in l-groups
No full textIn this paper we present some new versions of Brooks-Jewett and Dieudonne'-type theorems for l-group-valued measures.
Here the concepts of s-boundedness, sigma-additivity and regularity are formulated similarly as in the classical case, and not directly related to order sequences, regulators or similar objects. We use the tools of the Maeda-Ogasawara-Vulikh representation theorem and a technical lemma, which allows to prove some properties of l-group-valued measures using the corresponding ones of real-valued set functions
Un criterio di compattezza debole alla Dunford-Pettis
No full textIn this short paper we present a general elegant proof of a weakly compactness composite theorem for measure spaces, whose various parts can be traced back, in some form, to Dunford, Pettis, Nagumo and Tonelli. Also the construction of a comparison function is new, simple and particularly useful
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