PMA Rudin p.141
Rudine defined a curve $\gamma_3:[0,2\pi]\rightarrow \mathbb{C}:t\mapsto e^{2\pi i t sin(\frac{1}{t})}$.
It reallt doesn't make sense to define such a function since it is not defined at $t=0$.
What's actually Rudin intended?
This is how i guessed.
Let $\alpha$ be a continuous fuction defined on $(a,b]$.
Then define length of $\alpha$ as $\lim_{s\to a} \Lambda(\alpha\upharpoonright [s,b])$.
Then this problem makes sense.
However, is this definition generally used? Is there another widely being used definition of 'length of a curve on an open interval'?