The term "structure" in the title is used in the Bourbakist sense. Chapter 0 is devoted to the exposition of a certain notorious failure, or inadequacy, of currently used integration structures, including those presented in Book 5 of the Bourbaki treatise and in the well-known text of PR Halmos. In Section G of that chapter, the nature of the integration structures presented here is briefly described. This description is amplified somewhat in the pre-ambles to chapters 2, 3 and 4.
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