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Titlebook: Basic Real Analysis; Houshang H. Sohrab Textbook 20031st edition Birkhäuser Boston 2003 Arithmetic.Cardinal number.Counting.Equivalence.ca

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发表于 2025-3-21 16:35:07 | 显示全部楼层 |阅读模式
期刊全称Basic Real Analysis
影响因子2023Houshang H. Sohrab
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图书封面Titlebook: Basic Real Analysis;  Houshang H. Sohrab Textbook 20031st edition Birkhäuser Boston 2003 Arithmetic.Cardinal number.Counting.Equivalence.ca
影响因子.One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. .Basic Real Analysis. is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. .Key features include: .* A broad view of mathematics throughout the book .* Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter .* Elegant proofs .* Excellent choice of topics .* Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter .* Emphasis on monotone functions throughout .* Good development of integration theory .* Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis .* Solid preparation for deeper stud
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发表于 2025-3-21 21:24:20 | 显示全部楼层
Textbook 20031st editionand counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. .Basic Real Analysis. is a modern, systematic text that presents the fundamentals and touchsto
发表于 2025-3-22 04:03:06 | 显示全部楼层
Hierarchische Produktionsplanung und KANBAN same interval. ., ., . ℝ. Although we are studying . here, we should at least introduce the field ℂ of complex numbers and even use it in some definitions if this clarifies the concepts. Our presentation will be brief and most of the proofs are left as simple exercises for the reader.
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发表于 2025-3-22 09:38:16 | 显示全部楼层
tical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. .Basic Real Analysis. is a modern, systematic text that p
发表于 2025-3-22 16:03:45 | 显示全部楼层
Grundlagen der Produktionsplanung, not vector subspaces unless they pass through the origin. There is an important class of metric spaces, however, that is a natural framework for the extension of topological as well as algebraic properties of ℝ and ℂ : It is the class of ., which we now define. ., . . ℝ . ℂ . ., ., ., . ..
发表于 2025-3-22 20:40:39 | 显示全部楼层
Grundbegriffe der Produktionsplanung, the following . approach to the general case: Try to approximate the given function by step functions, find the areas corresponding to the latter functions as above, and . Our objective in this chapter is to provide a mathematically rigorous foundation for this intuitive approach. We begin with some basic definitions.
发表于 2025-3-22 21:36:45 | 显示全部楼层
Intention und Aufbau der Arbeit,measure and integral will therefore be extended and, since the proofs are in many cases almost identical, we may omit such proofs and assign them as exercises for the reader. ., .. Also recall that, in the set [-∞, ∞] of extended real numbers, we have ±∞ · 0:= 0.
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发表于 2025-3-23 07:26:35 | 显示全部楼层
General Measure and Probability,measure and integral will therefore be extended and, since the proofs are in many cases almost identical, we may omit such proofs and assign them as exercises for the reader. ., .. Also recall that, in the set [-∞, ∞] of extended real numbers, we have ±∞ · 0:= 0.
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