Probability Measures with Big Kernels
Keyword(s):
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.
1975 ◽
Vol 50
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pp. 435-435
2017 ◽
Vol 20
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pp. 1750023
1989 ◽
Vol 47
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pp. 307-312
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1997 ◽
Vol 20
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pp. 111-114
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2007 ◽
Vol 82
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pp. 1-9
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1980 ◽
Vol 03
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pp. 271-289
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1970 ◽
Vol 11
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pp. 417-420