Remark 31.1.1.label Since weak holomorphy is equivalent to strong holomorphy, most common results of scalar-valued holomorphic functions may be transferred to the vector valued case with little effort. Since this chapter represents my first attempt at learning complex analysis, and I happen to require vector-valued results, most results here are stated and proven in the vector-valued case. However, this is strictly unnecessary if one already knows the scalar-valued results.