Resumen de Doubling measures with doubling continuous part

Man-Li Lou, Min Wu

• We prove that every compact subset of of positive Lebesgue measure carries a doubling measure which is not purely atomic. Also, we prove that for every compact and nowhere dense subset of without isolated points and for every doubling measure on there is a countable set with and a doubling measure on such that . This shows that there are many doubling measures whose continuous part is doubling.