Abstract In this paper, we simplify the structure of L p of infinite dimensional spaces in terms of L p of finite dimensional ones via an analogue of inductive limit for the category of Banach spaces. This identification will facilitate the computations regarding functions defined in spaces of an infinite number of variables as we will see in some examples including applications to Gaussian measures and Feynman path integrals.

中文翻译：

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关于无穷维可积函数的空间

摘要 本文通过类比Banach空间范畴的归纳极限，将无限维空间的L p 的结构简化为有限维空间的L p 。正如我们将在一些例子中看到的，包括高斯测度和费曼路径积分的应用，这种识别将促进关于在无限数量变量空间中定义的函数的计算。