Geodesic
Some properties of the operator of the measure extension
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 114-127

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The operator defining for a measure on algebra of sets, the extension on the sigma-algebra generated by the given algebra is considered. On the basis of the representation of the extended measure in the minimax terms, the property of the isometric isomorphism for the above-mentioned operator for the traditional normalizations is established. Some properties connected with the preservation of order relations under the given operator are established.
Keywords: algebra of sets, measure, extension of measure, isometric isomorphism. 
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     author = {A. G. Chentsov},
     title = {Some properties of the operator of the measure extension},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {114--127},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_3_a9/}
}
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A. G. Chentsov. Some properties of the operator of the measure extension. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 114-127. http://geodesic.mathdoc.fr/item/VUU_2009_3_a9/