Abstract. The theorem we prove in this paper provides a unified and elementary method to prove various density theorems independent of the wellknown Lebesgue density theorem, but including density theorems like the hearts density theorem by Aversa and Preiss.

AMS Subject Classification (1991): 26A24, 26A99

Received March 3, 1997 and in revised form September 18, 1997. (Registered under 2645/2009.)