Rao, N.V. Israel J. Math. (1990) 70: 93. doi:10.1007/BF02807221
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 fxand fyeverywhere in G and the Cauchy Riemann equations fx +ify = 0are satisfied almost everywhere, then f is holomorphic in G. From our generalization of this theorem, we deduce a theroem of Sindalovskii  as a corollary and also answer some of the questions raised in . We note in this context that, as far as we know, Sindalovskii’s result is the best published to date in this area.