We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
@article{bwmeta1.element.bwnjournal-article-fmv147i1p61bwm, author = {Kenneth Kunen and Jan van Mill}, title = {Measures on Corson compact spaces}, journal = {Fundamenta Mathematicae}, volume = {146}, year = {1995}, pages = {61-72}, zbl = {0834.54014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv147i1p61bwm} }
Kunen, Kenneth; van Mill, Jan. Measures on Corson compact spaces. Fundamenta Mathematicae, Tome 146 (1995) pp. 61-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i1p61bwm/
[00000] [1] J. Cichoń, A. Kamburelis and J. Pawlikowski, On dense subsets of the measure algebra, Proc. Amer. Math. Soc. 94 (1985), 142-146. | Zbl 0593.28003
[00001] [2] M. Džamonja and K. Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), 41-54. | Zbl 0805.28008
[00002] [3] V. V. Fedorchuk, On the cardinality of hereditarily separable bicompacta, Dokl. Akad. Nauk SSSR 222 (1975), 302-305 (in Russian).
[00003] [4] D. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984. | Zbl 0551.03033
[00004] [5] P. Halmos, Measure Theory, Van Nostrand, 1968.
[00005] [6] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287.
[00006] [7] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108-111. | Zbl 0063.03723
[00007] [8] R. D. Mauldin, The existence of non-measurable sets, Amer. Math. Monthly 86 (1979), 45-46. | Zbl 0415.28002
[00008] [9] H. P. Rosenthal, On injective Banach spaces and the spaces for finite measures μ, Acta Math. 124 (1970), 205-248. | Zbl 0207.42803