Defining Integrals over R^R, R^N

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Integrals over R^R and R^N can be approached through concepts in Functional Analysis, particularly involving abstract Wiener spaces. The discussion highlights the integration of operators, which are typically linear or continuous, within infinite-dimensional spaces. Participants seek references to deepen their understanding of these integrals and their applications. The complexity of defining such integrals stems from the intricacies of infinite-dimensional analysis. Further exploration of the topic may yield additional insights and methodologies.
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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