0000000001333545
AUTHOR
Di Piazza, Luisa
showing 3 related works from this author
Approximation of Banach space valued Riemann type integrable functions by step functions
2008
In this talk we consider the possibility to approximate (with respect to some topology induced by the Alexiewicz norm) non absolutely integrable functions defined on the unit interval by step functions. In particular we show that any Henstock (respectively Henstock-Kurzweil-Pettis, Denjoy-Khintchine-Pettis) integrable functions can be scalarly approximate in the Alexiewicz norm by a sequence of step functions. Moreover the approximation may be done in the Alexiewicz norm if and only if the range of the integral is relatively norm compact (property which is automatically satisfied by the Henstock integrable functions). We also provide an example to show that, unlike the Pettis case, Henstock…
MR2553995 (2010h:26008): Mihail, Alexandru The Arzela-Ascoli theorem for partial defined functions. An. Univ. Bucureşti Mat. 57 (2008), no. 2, 259–26…
2008
In this paper the author gives a generalization of the Arzela-Ascoli theorem for partial defined functions, i.e., for functions defined in a nonempty subset of a metric space X and taking values in a metric space Y. To this end suitable definitions of local and uniform convergence for partial defined functions are introduced. As an application a different proof of a known result concerning the existence of Lipschitz selections for Lipschitz multifunctions is given. Reviewed by Luisa Di Piazza
MR2657294 (2011h:28021) Bensimhoun, Michael Change of variable theorems for the KH integral. Real Anal. Exchange 35 (2010), no. 1, 167–194. (Reviewer…
2010
From Reviews: 0 MR2657294 (2011h:28021) Bensimhoun, Michael(IL-HEBR) Change of variable theorems for the KH integral. (English summary) Real Anal. Exchange 35 (2010), no. 1, 167–194. 28B05 (26A42 46G10) PDF Clipboard Journal Article Make Link Let $({\scr E},{\scr F}, {\scr G})$(E,F,G) be a Banach triple and let $f\colon [a,b] \subset \overline{\Bbb R} \rightarrow {\scr E}$f:[a,b]⊂R−−→E, $\varphi \colon [a,b] \rightarrow {\scr F}$φ:[a,b]→F and $\psi\colon [c,d] \subset \overline{\Bbb R} \rightarrow [a,b]$ψ:[c,d]⊂R−−→[a,b] be given. The problem of change of variables in an integral consists in finding the best conditions under which the equality $$ \int_c^d f \circ \psi \cdot d(\varphi \circ …