Let be a quasicomplete locally convex Hausdorff space. Let be a locally compact Hausdorff space and let , is continuous and vanishes at infinity be endowed with the supremum norm. Starting with the Borel extension theorem for -valued -additive Baire measures on , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map to be weakly compact.
We state and prove a chain rule formula for the composition of a vector-valued function by a globally Lipschitz-continuous, piecewise function . We also prove that the map is continuous from into for the strong topologies of these spaces.
Let be a perfect compact set, a quasi-complete locally convex space over and a map. In this note we give a necessary and sufficient condition — in terms of differential quotients — for to have a holomorphic extension on a neighborhood of .
La presente Nota contiene una lista di -algebre reali di dimensione finita ed una lista di -algebre complesse di dimensione finita tali che: 1) due elementi distinti di ogni lista non sono mai -isomorfi; 2) ogni -algebra di dimensione finita reale (complessa) è —isomorfa su (su ) alla somma diretta, finita, di -algebre reali (complesse) elencate nella lista. In altre parole, diamo qui una classificazione completa delle —algebre reali e delle -algebre complesse di dimensione finita. Nel...
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.