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The uniform limit of Lipschitz functions on a Banach space*

Published online by Cambridge University Press:  09 April 2009

J. V. Herod
J. V. Herod
Affiliation:
Georgia Institute of TechnologyAtlanta, Georgia 30332, USA
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With R the set of real numbers and S a Banach space, let ℒ be the class of functions A from R × S to S which have following properties: (1) if B is a bounded subset of S then the family {A(·, P): P is in B} is equicontinuous; i.e., if t is a number and ε > 0 then there is a positive number δ such that if |s – t | < δ and P is in B then | A(s, P) – A(t, P)| < ε.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 325 - 331
Copyright
Copyright © Australian Mathematical Society 1973

References

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