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We study the integrals of real functions which are finite compositions of globally
subanalytic maps and real power functions. These functions have finiteness properties
very similar to those of subanalytic functions. Our aim is to investigate how such
finiteness properties can remain when taking the integrals of such functions. The main
result is that for almost all power maps arising in a -function, its
integration leads to a non-oscillating function. This can be seen as a generalization of
Varchenko...
We relate the notion of arc-analyticity and the one of analyticity on restriction to polynomial arcs and we prove that in the subanalytic setting, these two notions coincide.
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