Outer measures on a commutative ring induced by measures on its spectrum
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.
Keywords
outer measure; commutative ring; prime ideal; Carathéodory’s condition; ring of functions; unique factorization domain
References
2. Dudzik D., Skrzyński 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.
Instytut Matematyki, Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie Poland
Instytut Matematyki, Politechnika Krakowska Poland
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