Integration of semialgebraic functions and integrated Nash functions

DOI10.1007/s00209-012-1138-1zbMath1314.03038OpenAlexW2046046781MaRDI QIDQ379192

Tobias Kaiser

Publication date: 11 November 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-012-1138-1

zbMATH Keywords

ringso-minimalityalgebraic power seriesparameterized integralssemialgebraic functions

Mathematics Subject Classification ID

Integration of real functions of several variables: length, area, volume (26B15) Semialgebraic sets and related spaces (14P10) Model theory of ordered structures; o-minimality (03C64) Nash functions and manifolds (14P20) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items (7)

Global complexification of real analytic globally subanalytic functions ⋮ Integration of oscillatory and subanalytic functions ⋮ Counting imaginary quadratic points via universal torsors ⋮ On tameness of zonoids ⋮ Multivariate Puiseux Rings Induced by a Weierstrass System and Twisted Group Rings ⋮ Differentiability properties of log-analytic functions ⋮ 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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• Log-analytic nature of the volume of subanalytic sets
• Extending Tamm's theorem
• On the elementary theory of restricted elementary functions
• A preparation theorem for Weierstrass systems
• Measure and integration theory. Transl. from the German by Robert B. Burckel

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