Israel Journal of Mathematics

, Volume 70, Issue 1, pp 93–103 | Cite as

A generalization of the Looman-Menchoff theorem

  • N. V. Rao


In this paper we give a generalization of the classical Looman-Menchoff theorem:If f is a complex-valued continuous function of a complex variable in a domain G, f has partial derivatives f x and f y everywhere in G and the Cauchy Riemann equations f x +if y = 0are satisfied almost everywhere, then f is holomorphic in G. From our generalization of this theorem, we deduce a theroem of Sindalovskii [9] as a corollary and also answer some of the questions raised in [9]. We note in this context that, as far as we know, Sindalovskii’s result is the best published to date in this area.


Linear Continuity Vertical Strip Fourth Quadrant Essential Singularity Riemann Equation 
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Copyright information

© Hebrew University 1990

Authors and Affiliations

  • N. V. Rao
    • 1
  1. 1.Department of MathematicsUniversity of ToledoToledoUSA

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