A cylinder set measure on " E " is not actually a measure on " E " : it is a collection of measures defined on all finite-dimensional images of " E ".
42.
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.
43.
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;.
44.
Explicit representations for the cylinder sets can be gotten by noting that the string of values corresponds to a " q "-adic number, and thus, intuitively, the product topology resembles that of the real number line.
45.
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;.
46.
This algebra is then commonly written as ( \ Omega, \ mathcal { F } ) where the elements of \ mathcal { F } are the finite-length sequences of coin flips ( the cylinder sets ).
47.
It was a six-wheel design of Killingworth type; the first and last axles were driven by pistons in two vertical cylinders set in the boiler top, and a chain drive working on central sprocket wheels connected all three axles.
48.
The partition function, together with the Hamiltonian, are used to define a measure on the Borel ?-algebra in the following way : The measure of a cylinder set, i . e . an element of the base, is given by
49.
Instead of using a central oculus in each dome, as at the Palace of Ardashir and as shown in the bas relief found at Kuyunjik, lighting was provided by a number of hollow terracotta cylinders set into the domes at regular intervals.
50.
Which can also be identified with the set of basis for the open sets of the product topology are cylinder sets; the homeomorphism maps these to the subspace topology that the Cantor set inherits from the natural topology on the real number line.
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