Defining Integrals over R^R, R^N

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SUMMARY

Integrals over the spaces ##\mathbb R^{\mathbb R}## and ##\mathbb R^{\mathbb N}## are defined within the framework of Functional Analysis, specifically involving the integration of operators that are linear or continuous between infinite-dimensional spaces. The discussion highlights the relevance of abstract Wiener spaces in this context. For a comprehensive understanding, references to advanced texts in Functional Analysis are essential, particularly those that address integration in infinite dimensions.

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WWGD
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Hi,
Just curious: how does one define integrals over ##\mathbb R^{\mathbb R}, \mathbb R ^{\mathbb N} ##? I assume this must be a topic in Functional Analysis. I know a bit about abstract Wiener spaces; is there something else? And I assume the objects that are integrated are operators (linear, orat least continuous) between infinite dimensional spaces ( at least the domain of definition is infinite-dimensional). Hoping some one has a reference. Thanks.
 

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