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

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.

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.

@article{AIF_1981__31_2_137_0,
     author = {Christensen, J. P. Reus and Pachl, J. K.},
     title = {Measurable functionals on function spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {31},
     number = {2},
     year = {1981},
     pages = {137-152},
     doi = {10.5802/aif.832},
     zbl = {0437.46022},
     mrnumber = {82j:46035},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1981__31_2_137_0}
}
Christensen, J. P. Reus; Pachl, J. K. Measurable functionals on function spaces. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 137-152. doi : 10.5802/aif.832. http://www.numdam.org/item/AIF_1981__31_2_137_0/

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