Question

Show that \(\gamma: [0,1] \rightarrow \mathbb C\) is a Lipschitz function then \(\gamma\) is of bounded variation.
Please, help

Answer 1

@oldrin.bataku

Answer 2

\[\sum_{i=0}^{n -1}|\gamma(a_{i+1}) - \gamma(a_{i})| \leq \sum_{i=0}^{n-1}c\cdot |a_{i+1} - a_{i}|= \sum_{i=0}^{n-1}c\cdot (a_{i+1} - a_{i})=c\cdot(1-0)=c\]