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Every complete doubling metric space carries a doubling measure |
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| Authors: | Jouni Luukkainen Eero Saksman |
| Institution: | Department of Mathematics, P.O. Box~4 (Yliopistonkatu~5), FIN-00014 University of Helsinki, Finland ; Department of Mathematics, P.O. Box~4 (Yliopistonkatu~5), FIN-00014 University of Helsinki, Finland |
| Abstract: | We prove that a complete metric space  carries a doubling measure if and only if  is doubling and that more precisely the infima of the homogeneity exponents of the doubling measures on  and of the homogeneity exponents of  are equal. We also show that a closed subset  of  carries a measure of homogeneity exponent  . These results are based on the case of compact  due to Vol berg and Konyagin. |
| Keywords: | Doubling metric space homogeneous metric space Assouad dimension doubling measure homogeneous measure |
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