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SEPARATELY-ANALYTIC FUNCTION WITH SINGULARITIES SET OF POSITIVE LEBESGUE MEASURE

A.A.Atamuratov1, K.K.Rasulov2


In this work Shimoda’s theorem on separately-analytic functions is discussed and there is constructed an example of separately-analytic function with singularities set of positive Lebesgue measure. Proved that, separately-analytic functions satisfying Shimoda’s theorem on
can be represented by Hartogs’ series with holomorphic coefficients out of some nowhere dense compact subset of
.



https://doi.org/10.59251/2181-1296.v5.1351.1100

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