Correction: I wrote (regarding choosing a domain D in C on which log is defined and continuous): << More generally, D can be chosen to be any simply-connected region of the Riemann surface for log.

...

This should read instead: More generally, D can be chosen to be any bounded open subset of the Riemann surface for log. P.S. The 1-dimensional product integral can be adapted to work over curves in C as well. --Dan