Hartogs's theorem on separate holomorphicity: Difference between revisions

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''NB{{dablink|Note that the terminology is inconsistent and Hartogs' theorem may also mean [[Hartogs' lemma]] on removable singularities, the result on [[Hartogs number]] in axiomatic set theory, or [[Hartogs extension theorem]].''}}

In [[mathematics]], '''Hartogs' theorem''' is a fundamental result of [[Friedrich Hartogs]] in the theory of [[several complex variables]]. It states that for complex-valued functions ''F'' on '''C'''^''n'', with ''n'' > 1, being an [[analytic function]] in each variable ''z''_''i'', 1 ≤ ''i'' ≤ ''n'', while the others are held constant, is enough to prove that ''F'' is a [[continuous function]].