Theory of Functions of a Real Variable (Paperback)
I.P. Natanson
- 出版商: Dover Publications
- 出版日期: 2016-08-17
- 售價: $1,050
- 貴賓價: 9.8 折 $1,029
- 語言: 英文
- 頁數: 544
- 裝訂: Paperback
- ISBN: 048680643X
- ISBN-13: 9780486806433
下單後立即進貨 (約5~7天)
買這商品的人也買了...
-
$14,580$13,851 -
$4,680$4,446 -
$1,600$1,568 -
$520$411
相關主題
商品描述
<內容簡介>
Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series.
Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.
商品描述(中文翻譯)
原著分為兩卷,這本由著名的蘇聯數學家撰寫的已絕版作品,對實變函數理論進行了全面的研究。本書適合數學高年級本科生和研究生閱讀,內容清晰地介紹了積分理論和泛函分析的基礎知識。先備知識包括基礎分析的基礎和對無理數理論、極限理論、連續函數、黎曼積分和無窮級數的一些熟悉。第一卷涵蓋了無窮集合和點集、可測集合和函數、有界函數的勒貝格積分、平方可和函數、有限變差函數、斯蒂爾澤積分、絕對連續函數和不定勒貝格積分。第二卷涵蓋了奇異積分、三角級數、凸函數、二維空間中的點集、多變數可測函數及其積分、集合函數及其在積分理論中的應用、超限數、貝爾分類、勒貝格積分的某些推廣以及泛函分析的一些思想。許多章節都包含有挑戰性的習題。