Need help proving this and there should be a correction : square root of n! not m. Problem 9 (Extending Lipschitz functions). Assume A C Rm, and let ƒ : A → Rª beLipschitz. Show that there exists a Lipschitz function ƒ : Rm → R" such thatf = f on A,Lip(f) ≤ √m Lip(f).(1)(2)

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Answered: Problem 9 (Extending Lipschitz…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Problem 9 (Extending Lipschitz functions). Assume AC Rm, and let f : A → R be Lipschitz. Show that there exists a Lipschitz function f: Rm → Rn such that f = f on A, Lip(f) ≤ √m Lip(ƒ). (1) (2)