We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is algo shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.
@article{urn:eudml:doc:39246,
title = {Extensions of set functions.},
journal = {Mathware and Soft Computing},
volume = {10},
year = {2003},
pages = {5-16},
zbl = {1051.28002},
mrnumber = {MR2039214},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39246}
}
Ovchinnikov, Sergei V.; Falmagne, Jean Claude. Extensions of set functions.. Mathware and Soft Computing, Tome 10 (2003) pp. 5-16. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39246/