Borel complexity of the space of probability measures

Author:
Abhijit Dasgupta

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2441-2443

MSC (2000):
Primary 03E15, 60B05; Secondary 28A05

Published electronically:
January 23, 2001

MathSciNet review:
1823929

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Abstract | References | Similar Articles | Additional Information

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always *true* , where is the least ordinal such that is .

**1.**Alexander S. Kechris,*Classical descriptive set theory*, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR**1321597****2.**Alexander S. Kechris,*Measure and category in effective descriptive set theory*, Ann. Math. Logic**5**(1972/73), 337–384. MR**0369072****3.**A. Louveau and J. Saint-Raymond,*Borel classes and closed games: Wadge-type and Hurewicz-type results*, Trans. Amer. Math. Soc.**304**(1987), no. 2, 431–467. MR**911079**, 10.1090/S0002-9947-1987-0911079-0**4.**Yiannis N. Moschovakis,*Descriptive set theory*, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR**561709****5.**K. R. Parthasarathy,*Probability measures on metric spaces*, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR**0226684****6.**Steven E. Shreve,*Probability measures and the 𝐶-sets of Selivanovskij*, Pacific J. Math.**79**(1978), no. 1, 189–196. MR**526678**

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Additional Information

**Abhijit Dasgupta**

Email:
takdoom@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-05801-4

Keywords:
Descriptive set theory,
probability measures,
Borel complexity

Received by editor(s):
October 24, 1994

Received by editor(s) in revised form:
November 24, 1999

Published electronically:
January 23, 2001

Additional Notes:
Supported in part by NSF Grant # DMS-9214048.

Communicated by:
Andreas R. Blass

Article copyright:
© Copyright 2001
Abhijit Dasgupta, GNU GPL style copyleft