On the Carathéodory approach to the construction of a measure

Abstract

The Carathéodory theorem on the construction of a measure is generalized by replacing the outer measure with an approximation of it and generalizing the Carathéodory measurability. The new theorem is applied to obtain dynamically defined measures from constructions of outer measure approximations resulting from sequences of measurement pairs consisting of refining $\sigma$-algebras and measures on them which need not be consistent. A particular case when the measurement pairs are given by the action of an invertible map on an initial $\sigma$-algebra and a measure on it is also considered.

Polished version. Accepted for publication in Real Analysis Exchange

References in corpus (2)

• Erratum: Coding map for a contractive Markov system
• Lower bounds for the dynamically defined measures

Cited by in corpus (2)

• Lower bounds for the dynamically defined measures
• Erratum: Coding map for a contractive Markov system