Scenes from the History of Real FunctionsBirkhäuser, 2012. 12. 6. - 265페이지 To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt. |
목차
227 | 141 |
The derivative and the integral | 168 |
32 | 176 |
Nondifferentiable continuous functions | 212 |
| 235 | |
| 260 | |
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algebraic analytic expression applied arbitrary Arzelà Baire Borel calculus Cauchy class of functions connection continuous functions convergence almost everywhere convergence everywhere convergence in mean convergence in measure correspondence curve definite integral derivative differentiation and integration Dini Dirichlet discontinuous Egorov's Theorem equations Euler example exists finite number fn(x formula Fréchet func function f(x functional analysis functional dependence functions defined given Harnack History of Mathematics idea infinite infinitesimal interval introduced investigations kind of convergence Kolmogorov Lagrange Lebesgue Lebesgue integral Lebesgue's limit Lobachevskii mathematicians measurable functions measure zero method method of exhaustion nineteenth century nondifferentiable notion obtained paper point function problems proved question real variable relation representation Riemann integral Riesz Russian sense sequence of functions series of continuous set functions termwise differentiation termwise integration theorem theory of functions tion trigonometric series uniform convergence values W. H. Young Weierstrass Yushkevich