Euler integration over definable functions
نویسندگان
چکیده
منابع مشابه
Euler integration over definable functions.
We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in app...
متن کاملHadwiger Integration of Definable Functions
HADWIGER INTEGRATION OF DEFINABLE FUNCTIONS Matthew L. Wright Robert Ghrist, Advisor This thesis defines and classifies valuations on definable functionals. The intrinsic volumes are valuations on “tame” subsets of R, and by easy extension, valuations on functionals on R with finitely many level sets, each a “tame” subset of R. We extend these valuations, which we call Hadwiger integrals, to de...
متن کاملStatic Monotonicity Analysis for λ-Definable Functions over Lattices
We employ static analysis to examine monotonicity of functions defined over lattices in a λ-calculus augmented with constants, branching, meets, joins and recursive definitions. The need for such a verification procedure has recently arisen in our work with a static analyzer generator called Zoo, in which the specification of static analysis (input to Zoo) consists of finite-height lattice defi...
متن کاملOn the Euler characteristic of definable groups
We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point. ∗The author was supported b...
متن کاملThe Euler characteristic of definable groups
We show that in an arbitrary o-minimal structure the following are equivalent: (i) every infinite, definably compact, definably connected definable group G has o-minimal Euler characteristic E(G) zero; (ii) if H is a definable subgroup of a definably compact, definably connected, definable group G such that E(G/H) 6= 0, then G = ∪{gHg−1 : g ∈ G}; (iii) every infinite, definably compact, definab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2010
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0910927107