The Integrals of Lebesgue, Denjoy, Perron, and Henstock

Author: Russell A. Gordon

Publisher: American Mathematical Soc.

ISBN: 0821838059

Category: Mathematics

Page: 395

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Provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus. The Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which F is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. Contains over 230 exercises (with solutions) that illustrate and expand the material in the text.
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Trends in African Diaspora Mathematics Research

Author: Toka Diagana

Publisher: Nova Publishers

ISBN: 9781600213311

Category: Mathematics

Page: 173

View: 5329

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The African Diaspora presents mathematical research of highest rank. It offers a forum for mathematical research with some emphasis on the contributions of all African mathematicians and the rich connections between all African universities and those of other continents. This includes the Denjoy integral, equivalent cohomology, semi-linear equations, rational approximants, automorphic solutions and characterisations of mulitvariate exponential families.
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Mathematics Almost Everywhere: In Memory Of Solomon Marcus

Author: Bellow Alexandra,Calude Cristian S,Zamfirescu Tudor

Publisher: World Scientific

ISBN: 9813237325

Category: Computers

Page: 252

View: 5825

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The book is a collection of original papers, research and surveys, dedicated to the memory of the Romanian mathematician Solomon Marcus (1925-2016). Marcus published many papers and books in mathematical analysis, theoretical computer science, mathematical linguistics, poetics, theory of literature, semiotics, and several other fields less strongly connected to mathematics, like cultural anthropology, biology, history and philosophy of science, education. He exemplified an unimaginable richness of ideas. This volume intends to emphasize the mathematical fields in which Solomon Marcus worked, and demonstrate -- as he also did -- the interconnection between them. The authors who contribute to this volume are well-known experts in their fields. Most of them knew Solomon Marcus well, some even owed him for his decisive impulses for their careers and general development. With articles in so diverse areas, the volume will attract readers who would like to diversify their own knowledge or find unexpected connections with other topics. Contents: Logic, Complexity and Algebra: On Bases of Many-Valued Truth Functions (A Salomaa) Quasiperiods of Infinite Words (L Staiger) Early Romanian Contributions to Algebra and Polynomials (D Ştefănescu) Distributed Compression through the Lens of Algorithmic Information Theory: A Primer (M Zimand) Integrals, Operators, AF Algebras, Proof Mining and Monotone Nonexpansive Mappings: Monotonically Controlled Integrals (T Ball, D Preiss) Fine Properties of Duality Mappings (G Dincă) Primitive Ideal Spaces of Postliminal AF Algebras (A Lazar) An Application of Proof Miningto the Proximal Point Algorithm in CAT(0) Spaces (L Leuştean, A Sipoş) Generic Well-posedness of the Fixed Point Problem for Monotone Nonexpansive Mappings (S Reich, A J Zaslavski) Linguistics, Computer Science and Physics: Analytical Linguistics and Formal Grammars: Contributions of Solomon Marcus and Their Further Developments (M Burgin) A Contagious Creativity (Gh Păun) Entanglement through Path Identification (K Svozil) Solomon Marcus in Context: Memories about Solomon Marcus (A Bruckner) Memories With and About My Uncle (M Marcus) Index Readership: Graduate students and researchers. Keywords: Discrete Mathematics;Mathematical Analysis;Complexity Theory;Proof Mining;Mathematical Biology;Formal Languages;Theoretical Mechanics;Mathematical Linguistics;Theoretical PhysicsReview: Key Features: New results in a variety of mathematical areas including operator theory, measure theory, real and functional analysis, computable algebra, formal languages, proof mining in nonlinear analysis, theoretical mechanics, mathematical logic, and topical surveys in mathematical linguistics, complexity theory and computational biology The authors, coming from various parts of the world, are well-known experts in the areas of their contributions Interconnections between results and domains will make the volume not only informative, but also attractive and unique
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Henstock-Kurzweil Integration on Euclidean Spaces

Author: Tuo Yeong Lee

Publisher: World Scientific

ISBN: 9814324582

Category: Mathematics

Page: 314

View: 1915

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The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
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The Kurzweil-Henstock Integral and Its Differential

A Unified Theory of Integration on R and Rn

Author: Solomon Leader

Publisher: CRC Press

ISBN: 9780824705350

Category: Mathematics

Page: 276

View: 8169

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A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each section as well as appended sets of exercises.
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Integral

An Easy Approach After Kurzweil and Henstock

Author: Lee Peng Yee,Rudolf Vyborny

Publisher: Cambridge University Press

ISBN: 9780521779685

Category: Mathematics

Page: 311

View: 5147

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Textbook on the theory of integration. Suitable for beginning graduate and final year undergraduate students.
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SCMJ

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2528

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Mathematical Analysis and Applications

International Conference on Mathematical Analysis and Applications, Craiova, Romania, 23-24 September 2005

Author: V. Rădulescu,Constantin Niculescu (P.)

Publisher: Amer Inst of Physics

ISBN: 9780735403284

Category: Mathematics

Page: 167

View: 6599

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In these proceedings from the conference in September 2005, participants describe their work at the interface between mathematical physics, numerical analysis, optimal control and calculus of variations. Papers include work in nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems. Ind
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