A remark on separate holomorphy
Tom 174 / 2006
Studia Mathematica 174 (2006), 309-317
MSC: 32D05, 32D25.
DOI: 10.4064/sm174-3-5
Streszczenie
Let be a Riemann domain over {\mathbb C}^k\times{\mathbb C}^\ell. If X is a domain of holomorphy with respect to a family {\mathcal F}\subset{\mathcal O}(X), then there exists a pluripolar set P\subset{\mathbb C}^k such that every slice X_a of X with a\notin P is a region of holomorphy with respect to the family \{f|_{X_a}: f\in{\mathcal F}\}.
