On compact spaces carrying Radon measures of uncountable Maharam type

David Fremlin

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 3, page 295-304
  • ISSN: 0016-2736

Abstract

top
If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable L 1 space, then there is a continuous surjection from X onto [ 0 , 1 ] ω 1 .

How to cite

top

Fremlin, David. "On compact spaces carrying Radon measures of uncountable Maharam type." Fundamenta Mathematicae 154.3 (1997): 295-304. <http://eudml.org/doc/212239>.

@article{Fremlin1997,
abstract = {If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable $L^1$ space, then there is a continuous surjection from X onto $[0,1]^\{ω_1\}$.},
author = {Fremlin, David},
journal = {Fundamenta Mathematicae},
keywords = {compact Radon measure space; continuous surjection; Martin's axiom; continuum hypothesis},
language = {eng},
number = {3},
pages = {295-304},
title = {On compact spaces carrying Radon measures of uncountable Maharam type},
url = {http://eudml.org/doc/212239},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Fremlin, David
TI - On compact spaces carrying Radon measures of uncountable Maharam type
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 3
SP - 295
EP - 304
AB - If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable $L^1$ space, then there is a continuous surjection from X onto $[0,1]^{ω_1}$.
LA - eng
KW - compact Radon measure space; continuous surjection; Martin's axiom; continuum hypothesis
UR - http://eudml.org/doc/212239
ER -

References

top
  1. [1] W. W. Comfort and S. Negrepontis, Chain Conditions in Topology, Cambridge Univ. Press, 1982. 
  2. [2] M. Džamonja and K. Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), 41-54. Zbl0805.28008
  3. [3] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984. Zbl0551.03033
  4. [4] D. H. Fremlin, Large correlated families of positive random variables, Math. Proc. Cambridge Philos. Soc. 103 (1988), 147-162. Zbl0639.28006
  5. [5] D. H. Fremlin, Measure algebras, pp. 877-980 in [13]. 
  6. [6] D. H. Fremlin, Real-valued-measurable cardinals, pp. 151-304 in [9]. Zbl0839.03038
  7. [7] R. G. Haydon, On Banach spaces which contain l 1 ( τ ) and types of measures on compact spaces, Israel J. Math. 28 (1977), 313-324. Zbl0365.46020
  8. [8] R. G. Haydon, On dual L 1 -spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152. Zbl0407.46018
  9. [9] H. Judah (ed.), Set Theory of the Reals, Israel Math. Conf. Proc. 6, Bar-Ilan Univ., 1993. 
  10. [10] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287. 
  11. [11] K. Kunen and J. van Mill, Measures on Corson compact spaces, Fund. Math. 147 (1995), 61-72. Zbl0834.54014
  12. [12] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108-111. Zbl0063.03723
  13. [13] J. D. Monk (ed.), Handbook of Boolean Algebras, North-Holland, 1989. 
  14. [14] G. Plebanek, Nonseparable Radon measures and small compact spaces, Fund. Math. 153 (1997), 25-40. Zbl0905.28008

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.