On integration in complete bornological locally convex spaces
A generalization of I. Dobrakov’s integral to complete bornological locally convex spaces is given.
On integration of vector functions with respect to vector measures
We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name -integral. Our main result states that -integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable...
On intersections of sets of positive Lebesgue measure
On intersections of small perfect sets.
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On invariant functions for positive operators
On invariant measures for piecewise -transformations of the n-dimensional cube
On invariant measures for piecewise convex transformations
On invariant measures for some infinite-dimensional dynamical systems
On invariant measures for the tend map.
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.
On Invariant Measures, Minimal Sets and a Lemma of Margulies.
On invariant measures of nonlinear Markov processes.
On Ito-Nisio type theorems for DS-groups.
On joint distribution in quantum logics. I. Compatible observables
The notion of a joint distribution in -finite measures of observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
On joint distribution in quantum logics. II. Noncompatible observables
This paper i a continuation of the first part under the same title. The author studies a joint distribution in -finite measures for noncompatible observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system...
On Kakutani's Dichotomy Theorem for Infinitive Products of not Necessarily Independent Functions.
On Kalmbach measurability
In this note we show that, for an arbitrary orthomodular lattice , when is a faithful, finite-valued outer measure on , then the Kalmbach measurable elements of form a Boolean subalgebra of the centre of .
On Kantorovich's result on the symmetry of Dini derivatives
For , let be the set of points at which is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if is continuous, then is a “()-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that is a -strongly right porous set for an arbitrary . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a -strongly right porous set ...
On Kurzweil-Stieltjes integral in a Banach space
In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral exists if has a bounded semi-variation on and is regulated on We prove that this integral has sense also if is regulated on ...
On lattices and algebras of simple functions