Kernel associated with a cylindrical measure

1981 ◽  
pp. 51-84 ◽  
Author(s):  
Simone Chevet
Keyword(s):  
Cylindrical Measure

Probability Measures with Big Kernels

2001 ◽  
Vol 8 (2) ◽  
pp. 333-346
Author(s):  
Nguyen Duy Tien ◽  
V. Tarieladze
Keyword(s):  
Probability Measure ◽  
Vector Space ◽  
Topological Vector Space ◽  
Dual Space ◽  
Full Measure ◽  
Probability Measures ◽  
Infinite Dimensional ◽  
Cylindrical Measure ◽  
Second Category

Abstract It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [Kernel associated with a cylindrical measure, Springer-Verlag, 1981, p. 69] is solved by proving that the annihilator of the kernel of a measure μ coincides with the annihilator of μ if and only if the topology of μ-convergence in the dual space is essentially dually separated.

scholarly journals Accessible cylindrical measure and Bochner's theorem

1986 ◽  
Vol 67 (1) ◽  
pp. 115-125
Author(s):  
Yoshiaki Okazaki ◽  
Yasuji Takahashi
Keyword(s):  
Bochner’S Theorem ◽  
Bochner's Theorem ◽  
Cylindrical Measure

Separating kernel of cylindrical measure

1987 ◽  
Vol 5 (6) ◽  
pp. 397-399
Author(s):  
Y Okazaki ◽  
Y Takahashi
Keyword(s):  
Cylindrical Measure
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