This arrangement is particularly popular with twin or double cylinder sets, and can be used to carry larger sets of three or four cylinders and most rebreathers.
32.
However, it is important to understand that in the case of cylinder set measures, this is a requirement that is part of the definition, not a result.
33.
A single W-12 Lorraine-Dietrich engine was used with the cylinders set in three banks spaced 60?apart from one another, similar to the arrangement used in Napier engines.
34.
The restriction that the cylinder set be the intersection of a " finite " number of open cylinders is important; allowing infinite intersections generally results in a finer topology.
35.
Being cylinder sets, this means their projections onto have no finite subcover, and since each is compact, we can find a point that is not covered by the projections of onto.
36.
Cylinder set measures are in general "'not "'measures ( and in particular need not be classical Wiener measure on the set of continuous paths starting at the origin in Euclidean space.
37.
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.
38.
Cylinder sets over topological vector spaces are the core ingredient in the formal definition of the Feynman path integral or functional integral of quantum field theory, and the partition function of statistical mechanics.
39.
The complement of an open set is a closed set, but the complement of a cylinder set is a union of cylinders, and so cylinder sets are also closed, and are thus clopen.
40.
The complement of an open set is a closed set, but the complement of a cylinder set is a union of cylinders, and so cylinder sets are also closed, and are thus clopen.
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