Decomposition of group-valued additive set functions

Tim Traynor

Annales de l'institut Fourier (1972)

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

Abstract

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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.

How to cite

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Traynor, 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

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

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