Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

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Abstract

On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.

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  • [1] Atiyah M.F. MacDonald I.G. Introduction to Commutative Algebra Addison-Wesley Publishing Company Reading 1969.

  • [2] Dudzik D. Skrzynski M. An outer measure on a commutative ring Algebra Discrete Math. 21 (2016) no. 1 51-58.

  • [3] Federer H. Geometric Measure Theory Springer Berlin 1969.

  • [4] Halmos P.R. Measure Theory Springer New York 1976.

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