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It is shown that the 2 -Betti numbers of an amenable covering of a finite cell-complex can be approximated by ordinary Betti numbers of the finite Følner subcomplexes. This is a new proof, using simple homological arguments, of a recent result of Dodziuk and Mathai. Mathematics Subject Classification (1991). 20, 55, 57.doi:10.1007/s000140050081 fatcat:yp2z456izbflxdxeyyeijccf2a