Effective genericity and differentiability
Copyright policy )Effective genericity and differentiability
We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions.
Revision: added sections 6-8; minor corrections
- Radboud University Nijmegen Netherlands
- University of Turku Finland
Algebra and Topology, Classification of real functions; Baire classification of sets and functions, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Mathematics - Logic, Baire category, 1-genericity, Algorithmic randomness and dimension, FOS: Mathematics, Algebra en Topologie, Computation over the reals, computable analysis, Logic (math.LO), differentiability
Algebra and Topology, Classification of real functions; Baire classification of sets and functions, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Mathematics - Logic, Baire category, 1-genericity, Algorithmic randomness and dimension, FOS: Mathematics, Algebra en Topologie, Computation over the reals, computable analysis, Logic (math.LO), differentiability
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