Measures satisfying a refined doubling condition and absolute continuity
Measures satisfying a refined doubling condition and absolute continuity
It is shown that for certain subsets <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F subset-of double-struck upper R Superscript n"> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>⊂</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">F \subset {\mathbb {R}^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, two measures with support <italic>F</italic> satisfying a …