Geodesic
Products of Radon Measures: A Counter-Example
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 285-289

Voir la notice de l'article provenant de la source Cambridge University Press

I show that if X is the hyperstonian space of Lebesgue measure on [0,1], then there are open sets in X×X which are not measurable for the simple product outer measure. This answers a question of M. C. Godfrey and M. Sion. 
Fremlin, D. H. Products of Radon Measures: A Counter-Example. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 285-289. doi: 10.4153/CMB-1976-044-9
@article{10_4153_CMB_1976_044_9,
     author = {Fremlin, D. H.},
     title = {Products of {Radon} {Measures:} {A} {Counter-Example}},
     journal = {Canadian mathematical bulletin},
     pages = {285--289},
     year = {1976},
     volume = {19},
     number = {3},
     doi = {10.4153/CMB-1976-044-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-044-9/}
}
TY  - JOUR
AU  - Fremlin, D. H.
TI  - Products of Radon Measures: A Counter-Example
JO  - Canadian mathematical bulletin
PY  - 1976
SP  - 285
EP  - 289
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-044-9/
DO  - 10.4153/CMB-1976-044-9
ID  - 10_4153_CMB_1976_044_9
ER  - 
%0 Journal Article
%A Fremlin, D. H.
%T Products of Radon Measures: A Counter-Example
%J Canadian mathematical bulletin
%D 1976
%P 285-289
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-044-9/
%R 10.4153/CMB-1976-044-9
%F 10_4153_CMB_1976_044_9

[1] 1. Berberian, S. K., Measure and Integration, Addison-Wesley 1971. Google Scholar

[2] 2. Bourbaki, N., Éléments de mathématique VI—Intégration, chaps. I-IV. Hermann, 1952 (A.S.I. 1175). Google Scholar

[3] 3. Dixmier, J., Sur certains espaces considérées par M. H. Stone, Summa Brasil. Math. 2 (1951) 151–182. Google Scholar

[4] 4. Erdös, P. and Oxtoby, J. C., Partitions of the plane into sets having positive measure in every non-null measurable product set, Trans. Amer. Math. Soc. 79 (1955) 91–102. Google Scholar

[5] 5. Fremlin, D. H., Topological Riesz Spaces and Measure Theory, Cambridge Univ. Press, 1974. Google Scholar

[6] 6. Godfrey, M. C. and M. Sion, On product of Radón measures, Canad. Math. Bull. 12 (1968) 427–444. Google Scholar

[7] 7. Halmos, P. R., Measure Theory, Van Nostrand, 1950. Google Scholar

[8] 8. Munroe, M. E., Measure and Integration, Addison-Wesley, 1971. Google Scholar

Cité par Sources :