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The Complexity of Antidifferentiation, Denjoy Totalization, and Hyperarithmetic Reals

Kechris, Alexander S. (1987) The Complexity of Antidifferentiation, Denjoy Totalization, and Hyperarithmetic Reals. In: Proceedings of the International Congress of Mathematicians. American Mathematical Society , Providence, RI, pp. 307-313. ISBN 978-0-8218-0110-9.

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We consider real functions on the interval [0, 1]. Denote by Δ the set of derivatives; i.e., Δ = {ƒ:ƒ is a derivative} = {ƒ : ∃F: [0,1]→ R {F is differentiable and ƒ = F')}. If ƒ є Δ, any F with F' = ƒ is a primitive of ƒ and is uniquely determined up to a constant. To normalize, we denote by F(x) = ʃ^x)0 ƒ the unique primitive of ƒ with F(0) = 0. This is the original Newtonian concept of integration as the inverse operation of differentiation, i.e., antidifferentiation.

Item Type:Book Section
Additional Information:© 1987 International Congress of Mathematicians. Research partially supported by National Science Foundation Grant DMS-8416349.
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MathSciNet ReviewMR0934228
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ID Code:38894
Deposited By: Ruth Sustaita
Deposited On:11 Jun 2013 22:17
Last Modified:03 Oct 2019 05:01

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