View source for Thin set

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A subset  $  A $
of a domain  $  D \subset  \mathbf C  ^ {k} $
such that, for each point  $  z \in D $, 
there exists an open polydisc  $  \Delta ( z, r) \subset  D $
and a function  $  f $
which is holomorphic, not identically equal to zero, but which vanishes on  $  A \cap \Delta ( z, r) $.

====Comments====
Usually, being thin means being a subset of an [[Analytic set|analytic set]]. Cf. also [[Thinness of a set|Thinness of a set]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  R.C. Gunning,   H. Rossi,   "Analytic functions of several complex variables" , Prentice-Hall  (1965)  pp. Chapt. 1, Sect. C</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R.M. Range,   "Holomorphic functions and integral representation in several complex variables" , Springer  (1986)  pp. Chapt. 1, Sect. 3</TD></TR></table>