Complex borel structure inJC-algebras

1991 ◽  
Vol 206 (1) ◽  
pp. 225-232 ◽  
Author(s):  
L. J. Bunce ◽  
J. D. Maitland Wright
Keyword(s):  
Borel Structure

Borel Structure

1992 ◽  
pp. 405-425
Keyword(s):  
Borel Structure

scholarly journals The Borel structure of iterates of continuous functions

1989 ◽  
Vol 32 (3) ◽  
pp. 483-494 ◽  
Author(s):  
Paul D. Humke ◽  
M. Laczkovich
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Space Of Continuous Functions ◽  
Borel Structure ◽  
Image Position ◽  
Set Of Points ◽  
Positive Integers

Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.

scholarly journals On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation

1980 ◽  
Vol 43 (2) ◽  
pp. 251-260 ◽  
Author(s):  
B. S. Spahn
Keyword(s):  
Borel Structure

scholarly journals A Note on the Borel Structure of a Metrizable Choquet Simplex and of its Extreme Boundary.

1966 ◽  
Vol 19 ◽  
pp. 161 ◽  
Author(s):  
Erik M. Alfsen
Keyword(s):  
Choquet Simplex ◽  
Borel Structure

scholarly journals CONTINUITY OF UNIVERSALLY MEASURABLE HOMOMORPHISMS

2019 ◽  
Vol 7 ◽  
Author(s):  
CHRISTIAN ROSENDAL
Keyword(s):  
New York ◽  
Functional Analysis ◽  
Chromatic Number ◽  
Set Theory ◽  
Measure Theory ◽  
Polish Groups ◽  
Hamming Graph ◽  
Borel Structure ◽  
North Holland Publishing ◽  
Haar Null Sets

Answering a longstanding problem originating in Christensen’s seminal work on Haar null sets [Math. Scand. 28 (1971), 124–128; Israel J. Math. 13 (1972), 255–260; Topology and Borel Structure. Descriptive Topology and Set Theory with Applications to Functional Analysis and Measure Theory, North-Holland Mathematics Studies, 10 (Notas de Matematica, No. 51). (North-Holland Publishing Co., Amsterdam–London; American Elsevier Publishing Co., Inc., New York, 1974), iii+133 pp], we show that a universally measurable homomorphism between Polish groups is automatically continuous. Using our general analysis of continuity of group homomorphisms, this result is used to calibrate the strength of the existence of a discontinuous homomorphism between Polish groups. In particular, it is shown that, modulo $\text{ZF}+\text{DC}$ , the existence of a discontinuous homomorphism between Polish groups implies that the Hamming graph on $\{0,1\}^{\mathbb{N}}$ has finite chromatic number.

The Classification of Factors is not Smooth

1973 ◽  
Vol 25 (1) ◽  
pp. 96-102 ◽  
Author(s):  
E. J. Woods
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Explicit Construction ◽  
Countable Family ◽  
Borel Sets ◽  
Isomorphism Classes ◽  
Borel Structure

There is a natural Borel structure on the set F of all factors on a separable Hilbert space [3]. Let denote the algebraic isomorphism classes in F together with the quotient Borel structure. Now that various non-denumerable families of mutually non-isomorphic factors are known to exist [1; 6; 8; 10; 11; 12; 13], the most obvious question to be resolved is whether or not is smooth (i.e. is there a countable family of Borel sets which separate points). We answer this question negatively by an explicit construction.

scholarly journals Borel structure in groups and their duals

1957 ◽  
Vol 85 (1) ◽  
pp. 134-134 ◽  
Author(s):  
George W. Mackey
Keyword(s):  
Borel Structure

scholarly journals TheR-Borel structure on a Choquet simplex

1977 ◽  
Vol 73 (1) ◽  
pp. 221-226 ◽  
Author(s):  
Roger Smith
Keyword(s):  
Choquet Simplex ◽  
Borel Structure
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