Abstract

We consider Borel measures on separable Banach spaces that are limits of their finite-dimensional images in the weak topology. The class of Banach spaces on which all measures have this property is introduced. The specified property is proved for all measures from the closure in variation of the linear span of the set of measures absolutely continuous with respect to Gaussian measures. Connections with the approximation property and the stochastic approximation property are considered.

中文翻译：

---

论测度的有限维图像逼近

摘要

我们考虑在可分离 Banach 空间上的 Borel 测度，它们是弱拓扑中有限维图像的限制。介绍了所有测度都具有该性质的 Banach 空间类。从关于高斯测度绝对连续的测度集的线性跨度变化的闭包中证明了所有测度的指定属性。考虑与近似属性和随机近似属性的连接。