Geodesic
Note on Continuous and Purely Finitely Additive Set Functions
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 407-412

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DOI

The Sobczyk-Hammer respectively Yosida-Hewitt decomposition ([17], [19]) generates the class of continuous respectively purely finitely additive charges. In this paper, attention is limited to hereditable properties for these classes. It is proved that the property of continuity is preserved with respect to extensions and that if all extensions of a charge to a charge on a given field are continuous, then the original charge is continuous. An analogous heredity theorem for purely finite additivity holds true in the monogenic case.
DOI : 10.4153/CMB-1986-064-6
Mots-clés : 28A10 
Siebe, Wilfried. Note on Continuous and Purely Finitely Additive Set Functions. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 407-412. doi: 10.4153/CMB-1986-064-6
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     title = {Note on {Continuous} and {Purely} {Finitely} {Additive} {Set} {Functions}},
     journal = {Canadian mathematical bulletin},
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     year = {1986},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-064-6/}
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