The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes
The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes
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DOI：
10.1007/978-1-4419-5821-1_11
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发表时间：
1967-10
影响因子：
1.7
通讯作者：
R. Dudley
中科院分区：
文献类型：
--
作者：
R. Dudley
本文件的前两节是介绍性的，与标题的两个部分相对应。众所周知，在无限维希尔伯特空间H中没有完全类似的勒伯苏测度或哈尔测度，但需要H的子集的大小的某种测度。本文研究闭、有界、凸、对称（-xεCifxεC）的子集H.这样的集合C称为Banach球，因为它是其线性跨度上的完备Banach范数的单位球。在大多数情况下，本文C将是紧凑的。
The first two sections of this paper are introductory and correspond to the two halves of the title. As is well known, there is no complete analog of Lebesue or Haar measure in an infinite-dimensional Hilbert spaceH, but there is a need for some measure of the sizes of subsets ofH. In this paper we shall study subsetsCofHwhich are closed, bounded, convex and symmetric (—xεCifxεC). Such a setCwill be called aBanach ball, since it is the unit ball of a complete Banach norm on its linear span. In most cases in this paperCwill be compact.