Is there a simple (and not so restrictive) condition for a set to be an uniqueness set for the space of holomorphic functions defined on some open subset $U \subseteq \mathbb{C}^n$? By uniqueness set I mean a set such that any function vanishing on it must be the zero function.
I want to know if there is an analogous to the accumulation condition of the one dimensional case. What condition on the set would allow to obtain all the derivatives at one point?
Being open is sufficient and I believe having positive measure is enough too. But I guess that some weaker assumptions would be sufficient. Is there a sharp condition?
Any suggestions and/or references are welcome.