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• W2013505864 abstract "For any real function h ( t ) which is continuous and monotonic increasing for t > 0 with , Hausdorff (10) in 1918 denned a Carathéodory measure with respect to h ( t ) which has subsequently been known as Hausdorff measure. For analysing sets in Euclidean space, these measures have proved both useful and interesting. Given a real function Φ( t ) which is continuous and monotonic decreasing for t > 0 with , Frostman(9) in 1935 denned capacity with respect to Φ( t ). Lebesgue measure in Euclidean k -space is a special case of Hausdorff measure, and capacity with respect to Φ( t ) becomes logarithmic capacity or Newtonian capacity in the cases , Φ( t )=1/ t , respectively. The interrelationship between h -measure and Φ-capacity has been of interest in both directions: (i) in applications to function theory one may be able to determine whether or not a set has positive capacity by examining the h -measure for suitable h ( t ) (see, for example, (5)); (ii) it may be possible to determine the measure properties of a set from knowledge of its capacity (see, for example, (7) and (17))." @default.
• W2013505864 created "2016-06-24" @default.
• W2013505864 creator A5039973062 @default.
• W2013505864 date "1961-07-01" @default.
• W2013505864 modified "2023-09-26" @default.
• W2013505864 title "On the connexion between Hausdorff measures and generalized capacity" @default.
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• W2013505864 doi "https://doi.org/10.1017/s0305004100035581" @default.
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