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  "body": "\n## Summary\n\nA cylinder set measure on a topological vector space is a consistent family of [[probability measures|059TJN0NZ1]] on its finite-dimensional images.\nIt assigns a probability to every set that is described by finitely many linear coordinates.\nIt need not come from a countably additive measure on the whole space.\nCylinder set measures are the raw material for Gaussian measures and white noise in infinite dimensions.\n\n## Explanations\n\n### L1 human\n\nIn infinite dimensions one often knows how a random point looks through any finite number of linear measurements, but not yet as a whole.\nA cylinder set measure records exactly this: for each finite set of measurements, a probability law of the readings, and the laws fit together.\nFor example, on a Hilbert space one may ask that every unit vector direction gives a standard normal reading, independent for orthogonal directions.\nThis is a cylinder set measure, but it is not a true measure on the Hilbert space, because a random point would have infinite length.\n",
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