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BMO rational approximation and one-dimensional Hausdorff content

BMO rational approximation and one-dimensional Hausdorff content

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X subset-of bold upper C"> <mml:semantics> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">C</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">X \subset {\mathbf {C}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be compact and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f element-of upper V upper M upper O …