On Characterization of Absolutely Continuous Measures on Locally Compact Spaces.
On coincidence of Pettis and McShane integrability
R. Deville and J. Rodríguez proved that, for every Hilbert generated space , every Pettis integrable function is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space and a scalarly null (hence Pettis integrable) function from into , which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from (mostly) into spaces. We focus in more detail on the behavior...
On Compactness in L...(..., X) in the Weak Topology and in the Topology ...(L...(..., X), L...(..., X')).
On conability of singlevalued mappings
On control submeasures and measures
On convergences of signed states
On convex functions in c0(w1).
It is proved that no convex and Fréchet differentiable function on c0(w1), whose derivative is locally uniformly continuous, attains its minimum at a unique point.
On De Blasi's differentiation theory for multifunctions
On Denjoy type extensions of the Pettis integral
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
On Denjoy-Dunford and Denjoy-Pettis integrals
The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...
On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)
On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function
We improve a theorem of P.G. Georgiev and N.P. Zlateva on Gâteaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly Gâteaux differentiable bump function. In particular, our result implies the following theorem: If is a distance function determined by a closed subset of a Banach space with a uniformly Gâteaux differentiable norm, then the set of points of at which is not Gâteaux differentiable is not only a first category set, but it is even -porous...
On differentiation of metric projections in finite dimensional Banach spaces
On exhaustive vector measures.
On extension of Baire vector measures
On extension of vector polymeasures
On extension of vector polymeasures. II.
On Fréchet differentiability of convex functions on Banach spaces
Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function defined on a separable Banach space are studied. The conditions are in terms of a majorization of by a -smooth function, separability of the boundary for or an approximation of by Fréchet smooth convex functions.
On full derivatives
On functions with vanishing local derivative