Mathematika

Research Article

Fubini-type theorems for general measure constructions

Professor K. J. Falconera1 and Professor R. Daniel Mauldina2

a1 Department of Mathematics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland.

a2 Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A.

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.

(Received February 01 1999)

Key Words:

  • 28A80 MEASURE AND INTEGRATION; Classical measure theory; Fractals.