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→top: Remove link to Domain (mathematics) (which currently redirects to Domain of a function). The second paragraph of this article already does a good job explaining the term "___domain of integration". |
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{{distinguish|functional integration (neurobiology)}}
'''Functional integration''' is a collection of results in [[mathematics]] and [[physics]] where the
In an ordinary integral (in the sense of [[Lebesgue integration]]) there is a function to be integrated (the integrand) and a region of space over which to integrate the function (the ___domain of integration). The process of integration consists of adding up the values of the integrand for each point of the ___domain of integration. Making this procedure rigorous requires a limiting procedure, where the ___domain of integration is divided into smaller and smaller regions. For each small region, the value of the integrand cannot vary much, so it may be replaced by a single value. In a functional integral the ___domain of integration is a space of functions. For each function, the integrand returns a value to add up. Making this procedure rigorous poses challenges that continue to be topics of current research.
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