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Fubini-type theorems for general measure constructions

  • K. J. Falconer (a1) and R. Daniel Mauldin (a2)

Methods are used from descriptive set theory to derive Fubinilike results for the very general Method I and Method II (outer) measure constructions. Such constructions, which often lead to non-σ-finite measures, include Carathéodory and Hausdorff-type measures. Several questions of independent interest are encountered, such as the measurability of measures of sections of sets, the decomposition of sets into subsets with good sectional properties, and the analyticity of certain operators over sets. Applications are indicated to Hausdorff and generalized Hausdorff measures and to packing dimensions.

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[CM]D. Cenzer and R. D. Mauldin . Inductive definability: measure and category. Adv. Math., 38 (1980), 5590.

[FJ]K. J. Falconer and M. Järvenpää . Packing dimensions of sections of sets. Math. Proc. Cambridge Philos. Soc., 125 (1999), 89104.

[K]A. S. Kechris . Classical Descriptive Set Theory. Springer-Verlag (1995),.

[MM]P. Mattila and R. D. Mauldin . Measure and dimension functions: measurability and densities. Math. Proc. Cambridge Philos. Soc., 121 (1997), 81100.

[Ol]L. Olsen . A multifractal formalism. Adv. Math., 116 (1995), 82196.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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