Page 1 of 1
• Problem 3. Let || . || be any norm on R". Let D CR and let f:D + R". Prove, if f is Lipschitz on D (with respect to th
Posted: Wed May 11, 2022 10:07 pm
by answerhappygod
- Problem 3 Let Be Any Norm On R Let D Cr And Let F D R Prove If F Is Lipschitz On D With Respect To Th 1 (38.39 KiB) Viewed 23 times
• Problem 3. Let || . || be any norm on R". Let D CR and let f:D + R". Prove, if f is Lipschitz on D (with respect to the norm || D with Lipschitz constant K >0, then for any subset A CD, that the restriction of f to A, f|A: A + R", defined as f|A(a):= f(a) for a € A, is Lipschitz on A (with respect to the norm || - D with the same Lipschitz constant K.