# Decomposition of group-valued additive set functions

Annales de l'institut Fourier (1972)

- Volume: 22, Issue: 3, page 131-140
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topTraynor, Tim. "Decomposition of group-valued additive set functions." Annales de l'institut Fourier 22.3 (1972): 131-140. <http://eudml.org/doc/74086>.

@article{Traynor1972,

abstract = {Let $m$ be an additive function on a ring $H$ of sets, with values in a commutative Hausdorff topological group, and let $K$ be an ideal of $H$. Conditions are given under which $m$ can be represented as the sum of two additive functions, one essentially supported on $K$, the other vanishing on $K$. The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.},

author = {Traynor, Tim},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {3},

pages = {131-140},

publisher = {Association des Annales de l'Institut Fourier},

title = {Decomposition of group-valued additive set functions},

url = {http://eudml.org/doc/74086},

volume = {22},

year = {1972},

}

TY - JOUR

AU - Traynor, Tim

TI - Decomposition of group-valued additive set functions

JO - Annales de l'institut Fourier

PY - 1972

PB - Association des Annales de l'Institut Fourier

VL - 22

IS - 3

SP - 131

EP - 140

AB - Let $m$ be an additive function on a ring $H$ of sets, with values in a commutative Hausdorff topological group, and let $K$ be an ideal of $H$. Conditions are given under which $m$ can be represented as the sum of two additive functions, one essentially supported on $K$, the other vanishing on $K$. The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.

LA - eng

UR - http://eudml.org/doc/74086

ER -

## References

top- [1] C.E. RICKART, Decomposition of additive set functions, Duke Math. Jour., 10 (1943), 653-665. Zbl0063.06492MR5,232c
- [2] M. SION, Outer measures with values in a topological group, Proc. Lond. Math. Soc. (3), 19 (1969), 89-106. Zbl0167.14503MR39 #398
- [3] M. SION, Group-valued outer measures, International Congress of Mathematicians, Nice, 1970. Zbl0224.28008
- [4] T. TRAYNOR, Absolute continuity for group-valued measures (to appear), Can. Math. Bull., 1973. Zbl0289.28010MR50 #7475
- [5] T. TRAYNOR, A general Hewitt-Yosida Decomposition, (to appear). Can. Jour. Math. Zbl0219.46034

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.