- Art Gallery -

In mathematics, Osgood's lemma, introduced by William Fogg Osgood (1899), is a proposition in complex analysis. It states that a continuous function of several complex variables that is holomorphic in each variable separately is holomorphic. The assumption that the function is continuous can be dropped, but that form of the lemma is much harder to prove and is known as Hartogs' theorem.


Osgood, William F. (1899), "Note über analytische Functionen mehrerer Veränderlichen" (PDF), Mathematische Annalen, Springer Berlin / Heidelberg, 52: 462–464, doi:10.1007/BF01476172, ISSN 0025-5831

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License