Let D,G ⊂ ℂ be domains, let A ⊂ D, B ⊂ G be locally regular sets, and let X:= (D×B)∪(A×G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M̂ of the envelope of holomorphy X̂ of X such that any function separately holomorphic on X∖M extends to a holomorphic function on X̂ ∖M̂. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-3-8,
author = {Marek Jarnicki and Peter Pflug},
title = {Cross theorem},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {295-302},
zbl = {0993.32010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-3-8}
}
Marek Jarnicki; Peter Pflug. Cross theorem. Annales Polonici Mathematici, Tome 77 (2001) pp. 295-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-3-8/