Subdifferentials, Local ε‐Supports and Asplund Spaces

Equivalent formulations of some statements on subdifferentials and local e-supports of Ekeland and Lebourg are presented. A certain property of a Banach space concerning the local e-supports is shown to be separably determined. This fact is used to show that a Banach space is trustworthy in the sense of Ioffe if (and only if) it is Asplund.