Upper envelopes of inner premeasures
Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 401-422.

Le présent article revient sur un des thèmes initiés dans les dernières sections du célèbre article “Theory of capacities” de Choquet, paru en 1953-54. Il vise à établir des versions compréhensives dans l’esprit des concepts récemment développés par l’auteur pour la théorie de la mesure et de l’intégration.

The paper resumes one of the themes initiated in the final sections of the celebrated “Theory of Capacities” of Choquet 1953-54. It aims at comprehensive versions in the spirit of the author’s recent work in measure and integration.

@article{AIF_2000__50_2_401_0,
     author = {K\"onig, Heinz},
     title = {Upper envelopes of inner premeasures},
     journal = {Annales de l'Institut Fourier},
     pages = {401--422},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     doi = {10.5802/aif.1759},
     mrnumber = {2001h:28017},
     zbl = {0962.28001},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1759/}
}
TY  - JOUR
AU  - König, Heinz
TI  - Upper envelopes of inner premeasures
JO  - Annales de l'Institut Fourier
PY  - 2000
SP  - 401
EP  - 422
VL  - 50
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1759/
DO  - 10.5802/aif.1759
LA  - en
ID  - AIF_2000__50_2_401_0
ER  - 
%0 Journal Article
%A König, Heinz
%T Upper envelopes of inner premeasures
%J Annales de l'Institut Fourier
%D 2000
%P 401-422
%V 50
%N 2
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1759/
%R 10.5802/aif.1759
%G en
%F AIF_2000__50_2_401_0
König, Heinz. Upper envelopes of inner premeasures. Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 401-422. doi : 10.5802/aif.1759. http://www.numdam.org/articles/10.5802/aif.1759/

[1] W. Adamski, Capacity like set functions and upper envelopes of measures, Math. Ann., 229 (1977), 237-244. | MR | Zbl

[2] W. Adamski, On regular extensions of contents and measures, J. Math. Analysis Appl., 127 (1987), 211-225. | MR | Zbl

[3] B. Anger, Approximation of capacities by measures, in: Lecture Notes Math., 226, pp. 152-170, Springer, 1971.

[4] B. Anger, Kapazitäten und obere Einhüllende von Maßen. Math. Ann., 199 (1972), 115-130. | MR | Zbl

[5] B. Anger, Representation of capacities. Math. Ann., 229 (1977), 245-258. | MR | Zbl

[6] B. Anger and J. Lembcke, Hahn-Banach type theorems for hypolinear functionals, Math. Ann., 209 (1974), 127-152. | MR | Zbl

[7] G. Choquet, Theory of capacities, Annales Inst. Fourier, Grenoble, 5 (1953-1954), 131-295. | Numdam | MR | Zbl

[8] G. Choquet, Forme abstraite du théorème de capacitabilité, Annales Inst. Fourier, Grenoble, 9 (1959), 83-89. | Numdam | MR | Zbl

[9] C. Dellacherie, Quelques commentaires sur les prolongements de capacités, in: Lecture Notes Math., 191, 77-81, Springer, 1971. | Numdam

[10] C. Dellacherie, Ensembles Analytiques, Capacités, Mesures de Hausdorff, Lecture Notes Math., 295, Springer, 1972. | MR | Zbl

[11] B. Fuchssteiner and H. König, New versions of the Hahn-Banach theorem, in: Intern. Ser.Num. Math., 47, 255-266, Birkhäuser 1980. | MR | Zbl

[12] B. Fuglede, Capacity as a sublinear functional generalizing an integral, Danske Vid. Selsk. Mat. -Fys. Medd., 38 (1971), 1-44. | MR | Zbl

[13] P.R. Halmos, Measure Theory. Van Nostrand 1950. | MR | Zbl

[14] A. Horn and A. Tarski, Measures on Boolean algebras, Trans. Amer. Math. Soc., 64 (1948), 467-497. | MR | Zbl

[15] P.J. Huber and V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities, Ann. Statist., 1 (1973), 251-263. | MR | Zbl

[16] J. Kindler, A Mazur-Orlicztype theorem for submodular set functions, J. Math. Analysis Appl., 120 (1986), 533-546. | MR | Zbl

[17] H. König, On the abstract Hahn-Banach theorem due to Rodé, Aequat. Math., 34 (1987), 89-95. | MR | Zbl

[18] H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications, Springer, 1997. | Zbl

[19] H. König, Image measures and the so-called image measure catastrophe, Positivity, 1 (1997), 255-270. | MR | Zbl

[20] H. König, What are signed contents and measures? Math. Nachr., 204 (1999), 101-124. | MR | Zbl

[21] H. König, The product theory for inner premeasures, Note di Mat., to appear. | Zbl

[22] H. König, Measure and integration: Comparaison of old and new procedures, Arch. Math., 72 (1999), 192-205. | Zbl

[23] H. König, Measure and integration: Mutual generation of outer and inner premeasures, Annales Univ. Saraviensis, Ser. Math., 9 (1998), 99-122. | MR | Zbl

[24] H. König, Measure and integration: Integral representations of isotone functionals, Annales Univ. Saraviensis, Ser. Math., 9 (1998), 123-153. | MR | Zbl

[25] G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math., 31 (1978), 474-481. | MR | Zbl

[26] V. Strassen, Meßfehler und Information, Z. Wahrsch. Verw. Geb., 2 (1964), 273-305. | MR | Zbl

[27] F. Topsøe, Topology and Measure, Lecture Notes Math., 133, Springer, 1970. | Zbl

[28] F. Topsøe, On construction of measures, in: Topology and Measure I (Zinnowitz 1974) Part 2, 343-381, Univ. Greifswald 1978. | Zbl

[29] F. Topsøe, Radon measures, some basic constructions, in: Lecture Notes Math., 1033, 303-311, Springer, 1983. | MR | Zbl

Cité par Sources :