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:R²-->R, G(x,y)=(x,y³), is not density continuous. (See K. Ciesielski, W. Wilczynski, Density continuous transformations on $$R², 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.