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The Subdifferentiability Properties of Typical Functions inC[0, 1]

✍ Scribed by Xianfu Wang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
150 KB
Volume
218
Category
Article
ISSN
0022-247X

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✦ Synopsis

w x

Let C denote the Banach space of continuous real valued functions on 0, 1 with the uniform norm; Ρ¨ and Ρ¨ f denote the approximate subdifferential and Clarke a c subdifferential. It is proved that there exists a residual set A ; C such that for Ε½ . Ε½ . w x every f g A we have Ρ¨ f x s R s Ρ¨ f x for each x g 0, 1 . Moreover, every a c

Ε½ . function f g A is nowhere subdifferentially regular in 0, 1 .

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