ON MEASURES WITH THE DOUBLING CONDITION

Abstract

The author characterizes metric spaces that carry a nontrivial measure with the doubling condition 0 \qquad \mu(B(x, 2R)) \le C \mu(B(x, R)), $ SRC=http://ej.iop.org/images/0025-5726/30/3/A10/tex_im_1034_img3.gif/> where . In particular, such a measure exists on any compact set in . Bibliography: 14 titles.