gaussian cylinder set measure造句

• An alternative proof that the Gaussian cylinder set measure is not a measure uses the Cameron Martin theorem and a result on the quasi-invariance of measures.
• The canonical Gaussian cylinder set measure on an infinite-dimensional separable Hilbert space " H " does not correspond to a true measure on " H ".
• Alternatively, one may use the abstract Wiener space construction, in which classical Wiener measure ? is the canonical Gaussian cylinder set measure on the Cameron-Martin Hilbert space corresponding to " C " 0.
• The Gaussian cylinder set measure on " H " gives a cylinder set measure on the space of tempered distributions, which extends to a measure on the space of tempered distributions, " S " & prime;.
• The canonical Gaussian cylinder set measure on an infinite-dimensional Hilbert space can never be a " bona fide " measure; equivalently, the identity function on such a space cannot be " & gamma; "-radonifying.
• The Hilbert space " H " has measure 0 in " S " & prime;, by the first argument used above to show that the canonical Gaussian cylinder set measure on " H " does not extend to a measure on " H ".