Rademacher Theorem for Fréchet spaces

Caterina La Russa

Rademacher Theorem for Fréchet spaces

Matematica e Informatica

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a separable Fréchet space. In this paper we deﬁne a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fréchet space is Gateaux diﬀerentiable outside a set belonging to A.

Original language	English
Pages (from-to)	263-275
Number of pages	13
Journal	Quaestiones Mathematicae
Volume	33
Publication status	Published - 2010

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Cite this

@article{b5aca3a7ecdc42fcb2842007217496e9,

title = "Rademacher Theorem for Fr{\'e}chet spaces",

abstract = "Let X be a separable Fr{\'e}chet space. In this paper we deﬁne a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fr{\'e}chet space is Gateaux diﬀerentiable outside a set belonging to A.",

keywords = "Gateaux diﬀerentiability, Lipschitz maps, Rademacher theorem., Gateaux diﬀerentiability, Lipschitz maps, Rademacher theorem.",

author = "{La Russa}, Caterina",

year = "2010",

language = "English",

volume = "33",

pages = "263--275",

journal = "Quaestiones Mathematicae",

issn = "1607-3606",

publisher = "Taylor and Francis Ltd.",

}

TY - JOUR

T1 - Rademacher Theorem for Fréchet spaces

AU - La Russa, Caterina

PY - 2010

Y1 - 2010

N2 - Let X be a separable Fréchet space. In this paper we deﬁne a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fréchet space is Gateaux diﬀerentiable outside a set belonging to A.

AB - Let X be a separable Fréchet space. In this paper we deﬁne a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fréchet space is Gateaux diﬀerentiable outside a set belonging to A.

KW - Gateaux diﬀerentiability

KW - Lipschitz maps

KW - Rademacher theorem.

KW - Gateaux diﬀerentiability

KW - Lipschitz maps

KW - Rademacher theorem.

UR - http://hdl.handle.net/10447/51607

M3 - Article

SN - 1607-3606

VL - 33

SP - 263

EP - 275

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

ER -

Rademacher Theorem for Fréchet spaces

Abstract

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this