Hostname: page-component-cb9f654ff-65tv2 Total loading time: 0 Render date: 2025-08-27T20:51:41.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Fubini-type theorems for general measure constructions

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

K. J. Falconer  and
R. Daniel Mauldin
K. J. Falconer
Affiliation:
Department of Mathematics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland.
R. Daniel Mauldin
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A.
Get access

Abstract

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.

MSC classification

Secondary: 28A80: Fractals

Information

Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 251 - 265
Copyright
Copyright © University College London 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[CM]Cenzer, D. and Mauldin, R. D.. Inductive definability: measure and category. Adv. Math., 38 (1980), 55–90.CrossRefGoogle Scholar
[F]Falconer, K. J.. Fractal Geometry: Mathematical Foundations and Applications. John Wiley (1990),.Google Scholar
[FJ]Falconer, K. J. and Järvenpää, M.. Packing dimensions of sections of sets. Math. Proc. Cambridge Philos. Soc., 125 (1999), 89–104.CrossRefGoogle Scholar
[K]Kechris, A. S.. Classical Descriptive Set Theory. Springer-Verlag (1995),.CrossRefGoogle Scholar
[M]Mattila, P.. Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press (1995),.CrossRefGoogle Scholar
[MM]Mattila, P. and Mauldin, R. D.. Measure and dimension functions: measurability and densities. Math. Proc. Cambridge Philos. Soc., 121 (1997), 81–100.CrossRefGoogle Scholar
[Ol]Olsen, L.. A multifractal formalism. Adv. Math., 116 (1995), 82–196.CrossRefGoogle Scholar
[Ra]Raymond, J. Saint. Boréliens à coupes Kσ. Bull. Soc. Math. France, 104 (1976), 389–406.CrossRefGoogle Scholar
[Ro]Rogers, C. A., Hausdorff Measures. Cambridge University Press (1970; 2nd edn., 1998).Google Scholar
[SS]Sion, M. and Sjerve, D.. Approximation properties of measures generated by continuous set functions. Mathematika, 9 (1962), 145–156.CrossRefGoogle Scholar