Stability under integration of sums of products of real globally subanalytic functions and their logarithms

DOI10.1215/00127094-2010-213zbMath1216.26008arXiv0911.4373OpenAlexW2014185065MaRDI QIDQ627324

Daniel J. Miller, Raf Cluckers

Publication date: 28 February 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.4373

zbMATH Keywords

globally subanalytic functionsLebesgue's integrallogarithm of subanalytic functionstability under integration

Mathematics Subject Classification ID

Real-analytic and semi-analytic sets (14P15) Integration of real functions of several variables: length, area, volume (26B15) Semialgebraic sets and related spaces (14P10) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Model theory of ordered structures; o-minimality (03C64) Exponential and trigonometric functions (33B10)

Related Items (11)

Integration of oscillatory and subanalytic functions ⋮ Integration of semialgebraic functions and integrated Nash functions ⋮ Subgradient Sampling for Nonsmooth Nonconvex Minimization ⋮ On preparation theorems for R_{an, exp}-definable functions ⋮ Hölder-Łojasiewicz inequalities for volumes of tame objects ⋮ First order tameness of measures ⋮ Bounding the decay of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function ⋮ On tameness of zonoids ⋮ Differentiability properties of log-analytic functions ⋮ Restricted log-exp-analytic functions and some differentiability results ⋮ Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank

Cites Work

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• Intégrales asymptotiques et monodromie
• Analytic $p$-adic cell decomposition and integrals
• A preparation theorem for Weierstrass systems
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