Measurable functionals on function spaces

J. P. Reus Christensen; J. K. Pachl

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 2, page 137-152
  • ISSN: 0373-0956

Abstract

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We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.

How to cite

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Christensen, J. P. Reus, and Pachl, J. K.. "Measurable functionals on function spaces." Annales de l'institut Fourier 31.2 (1981): 137-152. <http://eudml.org/doc/74493>.

@article{Christensen1981,
abstract = {We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.},
author = {Christensen, J. P. Reus, Pachl, J. K.},
journal = {Annales de l'institut Fourier},
keywords = {measurable functional; function space; countably additive measure; Radon measure; K-analytic space; invariant functional; weak sequential completeness of spaces of measures},
language = {eng},
number = {2},
pages = {137-152},
publisher = {Association des Annales de l'Institut Fourier},
title = {Measurable functionals on function spaces},
url = {http://eudml.org/doc/74493},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Christensen, J. P. Reus
AU - Pachl, J. K.
TI - Measurable functionals on function spaces
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 2
SP - 137
EP - 152
AB - We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.
LA - eng
KW - measurable functional; function space; countably additive measure; Radon measure; K-analytic space; invariant functional; weak sequential completeness of spaces of measures
UR - http://eudml.org/doc/74493
ER -

References

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  2. [2] J. B. COOPER and W. SCHACHERMAYER, Uniform measures and co-Saks spaces, Proc. Internat. Seminar Functional Analysis, Rio de Janeiro 1978. Zbl0462.46014
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  15. [15] J. K. PACHL, Measures as functionals on uniformly continuous functions, Pacific J. Math., 82 (1979), 515-521. Zbl0419.28006MR80j:28012
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