標(biāo)題: Titlebook: Basic Real Analysis; Houshang H. Sohrab Textbook 20031st edition Birkh?user Boston 2003 Arithmetic.Cardinal number.Counting.Equivalence.ca [打印本頁] 作者: Grievous 時(shí)間: 2025-3-21 16:35
書目名稱Basic Real Analysis影響因子(影響力)
書目名稱Basic Real Analysis影響因子(影響力)學(xué)科排名
書目名稱Basic Real Analysis網(wǎng)絡(luò)公開度
書目名稱Basic Real Analysis網(wǎng)絡(luò)公開度學(xué)科排名
書目名稱Basic Real Analysis被引頻次
書目名稱Basic Real Analysis被引頻次學(xué)科排名
書目名稱Basic Real Analysis年度引用
書目名稱Basic Real Analysis年度引用學(xué)科排名
書目名稱Basic Real Analysis讀者反饋
書目名稱Basic Real Analysis讀者反饋學(xué)科排名
作者: 狼群 時(shí)間: 2025-3-21 21:24
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作者: PHONE 時(shí)間: 2025-3-22 04:03
Hierarchische Produktionsplanung und KANBAN same interval. ., ., . ?. Although we are studying . here, we should at least introduce the field ? 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.作者: Ordnance 時(shí)間: 2025-3-22 04:33 作者: grieve 時(shí)間: 2025-3-22 09:38
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作者: 不能平靜 時(shí)間: 2025-3-22 16:03
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 ? and ? : It is the class of ., which we now define. ., . . ? . ? . ., ., ., . ..作者: chemoprevention 時(shí)間: 2025-3-22 20:40
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.作者: 指耕作 時(shí)間: 2025-3-22 21:36
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.作者: WAIL 時(shí)間: 2025-3-23 01:32 作者: 懸掛 時(shí)間: 2025-3-23 07:26
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.作者: Choreography 時(shí)間: 2025-3-23 13:25 作者: 低能兒 時(shí)間: 2025-3-23 14:24
Limits of Functions,As was pointed out in Chapter 2, the central idea in analysis is that of ., which was introduced and studied for . of real numbers, i.e., for functions . : ? → ?. In particular, the behavior of the term . := .(.) was studied under the assumption that the element . in the domain of our sequence was ..作者: conjunctivitis 時(shí)間: 2025-3-23 20:10 作者: 碎石頭 時(shí)間: 2025-3-23 23:53
978-1-4612-6503-0Birkh?user Boston 2003作者: Leaven 時(shí)間: 2025-3-24 03:12
,Topology of ? and Continuity,., it satisfies the nine axioms . – ., . – . and . listed at the beginning of Chapter 2. Given this field structure, the most (.) . functions ? : ? → ? are those that are . to the field properties; i.e., . them. Such maps are called the . of the field ?.作者: 食物 時(shí)間: 2025-3-24 07:59 作者: 傳授知識(shí) 時(shí)間: 2025-3-24 11:55
,The Lebesgue Integral (F. Riesz’s Approach),n are numerous and we shall not go into a detailed explanation of them. Probably the most important among them is that the space of all Riemann integrable fuctions on a compact interval [., .] ? ? is . with respect to the natural “metric”: 作者: 分期付款 時(shí)間: 2025-3-24 16:18 作者: 問到了燒瓶 時(shí)間: 2025-3-24 19:02
https://doi.org/10.1007/978-3-8349-8227-8n most cases, however, the proofs are given in appendices and omitted from the main body of the course. To give rigorous proofs of the basic theorems on convergence, continuity, and differentiability, one needs a precise definition of real numbers. One way to achieve this is to start with the . of r作者: puzzle 時(shí)間: 2025-3-24 23:46 作者: 雀斑 時(shí)間: 2025-3-25 05:44
Gegenstand der Produktionsplanung, abstract .; i.e., a set on which the concept of . (or .) can be defined. Indeed, as we have already seen, the basic concept of . which we studied in Chapters 2 and 3, and used to define (in Chapter 4) the related concept of continuity, is defined in terms of .. Let us recall that the distance betwe作者: 去世 時(shí)間: 2025-3-25 09:47
Grundbegriffe der Produktionsplanung,l variable, the derivative may be interpreted as an extension of the notion of . defined for (nonvertical) straight lines. Recall that a (nonvertical) straight line is the graph of an . ? . + ., where ., . are real constants and . is the slope of the line. Now, if .(.) := . + . ?. ∈ ?, then, for any作者: Incorruptible 時(shí)間: 2025-3-25 14:17
Grundbegriffe der Produktionsplanung,-valued function of a real variable, this integral extends the notion of ., defined initially for . For a . constant function .(.) := . ?. ∈ [., .], the area of the rectangle bounded by the graph of ., the .-axis, and the vertical lines . = . and . = ., is defined to be the non-negative number . := 作者: 倔強(qiáng)一點(diǎn) 時(shí)間: 2025-3-25 19:24 作者: Nefarious 時(shí)間: 2025-3-25 22:07 作者: 極大痛苦 時(shí)間: 2025-3-26 00:15
https://doi.org/10.1007/978-3-322-87580-8n are numerous and we shall not go into a detailed explanation of them. Probably the most important among them is that the space of all Riemann integrable fuctions on a compact interval [., .] ? ? is . with respect to the natural “metric”: 作者: ABASH 時(shí)間: 2025-3-26 06:11 作者: LUDE 時(shí)間: 2025-3-26 12:16 作者: Rotator-Cuff 時(shí)間: 2025-3-26 14:31 作者: 脫落 時(shí)間: 2025-3-26 19:38
http://image.papertrans.cn/b/image/181132.jpg作者: 流浪 時(shí)間: 2025-3-26 23:01 作者: 雪上輕舟飛過 時(shí)間: 2025-3-27 04:14 作者: 簡(jiǎn)略 時(shí)間: 2025-3-27 06:24
https://doi.org/10.1007/978-3-322-87580-8n are numerous and we shall not go into a detailed explanation of them. Probably the most important among them is that the space of all Riemann integrable fuctions on a compact interval [., .] ? ? is . with respect to the natural “metric”: 作者: Nucleate 時(shí)間: 2025-3-27 09:35
https://doi.org/10.1007/978-3-642-57987-5en chosen, especially when complements of sets (to be defined below) are involved in the discussion. Before defining the basic operations on sets, let us introduce a notation which will be used throughout the book.作者: FLAGR 時(shí)間: 2025-3-27 17:06
https://doi.org/10.1007/978-3-8349-8227-8their . Here, the most important concept is that of a .. It will be used in Appendix A for a brief discussion of Cantor’s construction of real numbers from the Cauchy sequences in the set ? of rational numbers. The properties of sequences will be used in a short section on infinite series of real nu作者: palpitate 時(shí)間: 2025-3-27 19:05
Gegenstand der Produktionsplanung,oint, convergent sequence and Cauchy sequence. We then defined the concept of limit for general real-valued functions of a real variable, and proved that such limits can also be defined in terms of limits of sequences. Also, before introducing the related notion of ., we introduced (in Chapter 4) th作者: 否認(rèn) 時(shí)間: 2025-3-27 23:52
https://doi.org/10.1007/978-3-322-87580-8erested in a larger class of functions containing simultaneously .. One of our goals in this chapter will be to introduce and study this class. Although we start with F. Riesz’s definition of a measurable function, we shall later give the more general definitions of ., ., . and prove the equivalence作者: Brocas-Area 時(shí)間: 2025-3-28 03:53 作者: Strength 時(shí)間: 2025-3-28 07:55 作者: 反省 時(shí)間: 2025-3-28 14:04 作者: Extemporize 時(shí)間: 2025-3-28 16:27
Lebesgue Measure,erested in a larger class of functions containing simultaneously .. One of our goals in this chapter will be to introduce and study this class. Although we start with F. Riesz’s definition of a measurable function, we shall later give the more general definitions of ., ., . and prove the equivalence作者: Tracheotomy 時(shí)間: 2025-3-28 21:08
Textbook 20031st editioninto 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作者: 吊胃口 時(shí)間: 2025-3-28 23:32
velopment 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 stud978-1-4612-6503-0978-0-8176-8232-3作者: 全等 時(shí)間: 2025-3-29 06:03 作者: MORPH 時(shí)間: 2025-3-29 10:56
Sequences and Series of Real Numbers,n most cases, however, the proofs are given in appendices and omitted from the main body of the course. To give rigorous proofs of the basic theorems on convergence, continuity, and differentiability, one needs a precise definition of real numbers. One way to achieve this is to start with the . of r作者: 定點(diǎn) 時(shí)間: 2025-3-29 13:04 作者: FACT 時(shí)間: 2025-3-29 17:57 作者: osteopath 時(shí)間: 2025-3-29 22:44 作者: GLEAN 時(shí)間: 2025-3-30 01:54 作者: RADE 時(shí)間: 2025-3-30 06:38
Sequences and Series of Functions,asier to investigate. We have already done this on a few occasions. For example, in Chapter 4, we looked at the . approximation of continuous functions by step, piecewise linear, and polynomial functions. Also, in Chapter 7, we proved that each bounded continuous function on a closed bounded interva作者: 打算 時(shí)間: 2025-3-30 08:20
Normed and Function Spaces,cause a metric space need not be an . or even a .. Any (nonempty) subset of a metric space is again a metric space with the metric it borrows from the ambient space. Thus, curves and surfaces in the Euclidean space ?. are metric spaces but are almost never . of ?.. Even straight lines and planes are
