# Thin set

From Encyclopedia of Mathematics

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. Cf. also Thinness of a set.

#### References

[a1] | R.C. Gunning, H. Rossi, "Analytic functions of several complex variables" , Prentice-Hall (1965) pp. Chapt. 1, Sect. C |

[a2] | R.M. Range, "Holomorphic functions and integral representation in several complex variables" , Springer (1986) pp. Chapt. 1, Sect. 3 |

**How to Cite This Entry:**

Thin set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Thin_set&oldid=48965

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article