In the paper it is proved that the complex analytic functions are
(ordinarily) density continuous.
This stay in contrast
with the fact that even such a simple function as G:**R**^{2}-->**R**,
G(x,y)=(x,y^{3}), is not density continuous.
(See K. Ciesielski, W. Wilczynski,
Density continuous transformations on
$$**R**^{2},
* Real Anal. Exchange 20 * (1994-95), 102-118.)
We will also characterize those analytic functions which are strongly
density continuous at the given point a in the complex plane **C**.
From this we conclude that
a complex analytic function f
is strongly density continuous if and only if f(z)= a + b z, where
a and b are in **C** and b is either real or imaginary.

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**Last modified April 24, 1999.**