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  "body": "\n## Summary\n\nAn abstract Wiener space is a [[Hilbert space|HM2HHE3J51]] sitting densely inside a larger [[Banach space|06GZ956657]].\nThe standard Gaussian [[cylinder set measure|G95YDNFXQN]] of the Hilbert space must become a true [[Gaussian measure|P0DV2TCH1N]] on the Banach space.\nThe notion was introduced by Leonard Gross.\nIt is the general frame for Wiener measure, Malliavin calculus and Gaussian free fields.\n\n## Explanations\n\n### L1 human\n\nThere is no standard Gaussian measure on an infinite-dimensional Hilbert space: a typical point would have infinite length.\nThe fix is to enlarge the space, with a weaker norm, until the typical points fit.\nThe classical example is Brownian motion.\nThe Hilbert space is the space of paths with square-integrable derivative, and the larger space is the space of all continuous paths, where Brownian paths actually live.\n",
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