If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable space, then there is a continuous surjection from X onto .
@article{bwmeta1.element.bwnjournal-article-fmv154i3p295bwm, author = {David Fremlin}, title = {On compact spaces carrying Radon measures of uncountable Maharam type}, journal = {Fundamenta Mathematicae}, volume = {154}, year = {1997}, pages = {295-304}, zbl = {0894.28007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv154i3p295bwm} }
Fremlin, David. On compact spaces carrying Radon measures of uncountable Maharam type. Fundamenta Mathematicae, Tome 154 (1997) pp. 295-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv154i3p295bwm/
[00000] [1] W. W. Comfort and S. Negrepontis, Chain Conditions in Topology, Cambridge Univ. Press, 1982.
[00001] [2] M. Džamonja and K. Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), 41-54. | Zbl 0805.28008
[00002] [3] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984. | Zbl 0551.03033
[00003] [4] D. H. Fremlin, Large correlated families of positive random variables, Math. Proc. Cambridge Philos. Soc. 103 (1988), 147-162. | Zbl 0639.28006
[00004] [5] D. H. Fremlin, Measure algebras, pp. 877-980 in [13].
[00005] [6] D. H. Fremlin, Real-valued-measurable cardinals, pp. 151-304 in [9]. | Zbl 0839.03038
[00006] [7] R. G. Haydon, On Banach spaces which contain and types of measures on compact spaces, Israel J. Math. 28 (1977), 313-324. | Zbl 0365.46020
[00007] [8] R. G. Haydon, On dual -spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152. | Zbl 0407.46018
[00008] [9] H. Judah (ed.), Set Theory of the Reals, Israel Math. Conf. Proc. 6, Bar-Ilan Univ., 1993.
[00009] [10] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287.
[00010] [11] K. Kunen and J. van Mill, Measures on Corson compact spaces, Fund. Math. 147 (1995), 61-72. | Zbl 0834.54014
[00011] [12] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108-111. | Zbl 0063.03723
[00012] [13] J. D. Monk (ed.), Handbook of Boolean Algebras, North-Holland, 1989.
[00013] [14] G. Plebanek, Nonseparable Radon measures and small compact spaces, Fund. Math. 153 (1997), 25-40. | Zbl 0905.28008