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Integration on Infinite-Dimensional Spaces

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Functional Analysis and the Feynman Operator Calculus

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Abstract

This chapter is required for the foundations of infinite-dimensional analysis. It is assumed that the reader is conversant with Lebesgue measure on \(\mathbb{R}^{n}\), including the standard limit theorems, inequalities, convolution, Fourier transform theory, and Fubini’s theorem. With this in mind, we offer a parallel treatment on infinite-dimensional spaces, with a theorem proof protocol. The proof of any theorem that is the same as on \(\mathbb{R}^{n}\) is omitted. We have also added a few interesting topics, which are discussed more fully below. We do not include any exercises, however, any serious question could lead to a research problem. (This statement applies to all chapters except Chaps. 1 and 4.)

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Authors and Affiliations

  1. Departments of Electrical and Computer Engineering, Howard University, Washington, DC, USA

    Tepper L. Gill & Woodford Zachary

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  1. Tepper L. Gill
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  2. Woodford Zachary
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Gill, T.L., Zachary, W. (2016). Integration on Infinite-Dimensional Spaces. In: Functional Analysis and the Feynman Operator Calculus. Springer, Cham. https://doi.org/10.1007/978-3-319-27595-6_2

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