HAUSDORFF MEASURES AND DIMENSION ON R-INFINITY

We consider the Hausdorff measures H-s, 0 less than or equal to s < in finity, defined on R-infinity = Pi(i=1)(infinity) R with the topology induced by the metric rho(x,y) = =1)Sigma(infinity)\x(i)-y(i)\/2(i)(1\x(i)-y(i)\), for all x=(x(i))(i=1)(infinity), y=(y(i))(i=1)(infinity) is an element of R-infinity. We study its properties, their relation to the ''Lebesgue measure'' defined on R-infinity by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some example s.