Authors: Johan Noldus
We engage in an approach towards integration theory divorced from measure theory concentrating on the dierentiable functions instead of the measurable ones. In a sense, we do for \measure theory" what dierential geometry does for topology; the nal goal of this paper being the rigorous denition of a generalization of the Feynman path integral. The approach taken is an axiomatic one in which it is more important to understand relationships between certain quantities rather than to calculate them exactly. In a sense, this is how the eld of algebraic geometry is developed in opposition to the study of partial dierential equations where in the latter case, the stress is unfortunately still too much on the construction of explicit solutions rather than on structural properties of and between solutions.
Comments: 5 Pages.
[v1] 2016-07-13 11:02:35
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