Properties of Orlicz-Pettis or Nikodym type and barrelledness conditions
Annales de l'Institut Fourier, Volume 28 (1978) no. 3, p. 67-85

An Orlicz-Pettis type property for vector measures and also the “Uniform Boundedness Principle” are shown to fail without local convexity assumption. The author asks under which generalized convexity hypotheses these properties remain true. This problem is expressed in terms of barrelledness type conditions.

On met en défaut des propriétés de type Orlicz-Pettis et de “bornitude uniforme” pour des mesures à valeurs dans certains espaces non localement convexes. On demande, en termes de conditions de tonnelage, quelles hypothèses de convexité généralisée assurent la validité de ces propriétés.

@article{AIF_1978__28_3_67_0,
     author = {Turpin, Philippe},
     title = {Properties of Orlicz-Pettis or Nikodym type and barrelledness conditions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {28},
     number = {3},
     year = {1978},
     pages = {67-85},
     doi = {10.5802/aif.701},
     zbl = {0344.46096},
     mrnumber = {80d:46080},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1978__28_3_67_0}
}
Turpin, Philippe. Properties of Orlicz-Pettis or Nikodym type and barrelledness conditions. Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 67-85. doi : 10.5802/aif.701. http://www.numdam.org/item/AIF_1978__28_3_67_0/

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