no. 2
Measurable functionals on function spaces
Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 137-152.

Sur certains espaces de fonctions, chaque forme mesurable est une mesure; ceci renforce les résultats connus qui affirment que certains espaces de mesures sont faiblement séquentiellement complets. Nous tirons plusieurs conséquences dans la forme suivante : si l’espace des formes invariantes sur un espace de fonctions est séparable, alors chaque forme invariante est une mesure.

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.

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     title = {Measurable functionals on function spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {137--152},
     publisher = {Institut Fourier},
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     volume = {31},
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     year = {1981},
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Christensen, J. P. Reus; Pachl, J. K. Measurable functionals on function spaces. Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 137-152. doi : 10.5802/aif.832. https://aif.centre-mersenne.org/articles/10.5802/aif.832/

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