{"product_id":"measure-and-integration-hardback","title":"Measure and Integration - Hardback","description":"\u003cp\u003eThis concise text is intended as an introductory course in measure and integration\u003cem\u003e.\u003c\/em\u003e It covers essentials of the subject, providing ample motivation for new concepts and theorems in the form of discussion and remarks, and with many worked-out examples. \u003c\/p\u003e\u003cp\u003eThe novelty of \u003cstrong\u003eMeasure and Integration: A First Course\u003c\/strong\u003e is in its style of exposition of the standard material in a student-friendly manner. New concepts are introduced progressively from less abstract to more abstract so that the subject is felt on solid footing. The book starts with a review of Riemann integration as a motivation for the necessity of introducing the concepts of measure and integration in a general setting. Then the text slowly evolves from the concept of an outer measure of subsets of the set of real line to the concept of Lebesgue measurable sets and Lebesgue measure, and then to the concept of a measure, measurable function, and integration in a more general setting. Again, integration is first introduced with non-negative functions, and then progressively with real and complex-valued functions. A chapter on Fourier transform is introduced only to make the reader realize the importance of the subject to another area of analysis that is essential for the study of advanced courses on partial differential equations.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eKey Features\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eNumerous examples are worked out in detail.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eLebesgue measurability is introduced only after convincing the reader of its necessity. \u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eIntegrals of a non-negative measurable function is defined after motivating its existence as limits of integrals of simple measurable functions. \u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eSeveral inquisitive questions and important conclusions are displayed prominently. \u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eA good number of problems with liberal hints is provided at the end of each chapter. \u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003eThe book is so designed that it can be used as a text for a one-semester course during the first year of a master's program in mathematics or at the senior undergraduate level.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAbout the Author\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eM. Thamban Nair \u003c\/b\u003eis a professor of mathematics at the Indian Institute of Technology Madras, Chennai, India. He was a post-doctoral fellow at the University of Grenoble, France through a French government scholarship, and also held visiting positions at Australian National University, Canberra, University of Kaiserslautern, Germany, University of St-Etienne, France, and Sun Yat-sen University, Guangzhou, China. \u003c\/p\u003e\u003cp\u003eThe broad area of Prof. Nair’s research is in functional analysis and operator equations, more specifically, in the operator theoretic aspects of inverse and ill-posed problems. Prof. Nair has published more than 70 research papers in nationally and internationally reputed journals in the areas of spectral approximations, operator equations, and inverse and ill-posed problems. He is also the author of three books: \u003ci\u003eFunctional Analysis: A First Course \u003c\/i\u003e(PHI-Learning, New Delhi), \u003ci\u003eLinear Operator Equations: Approximation and Regularization \u003c\/i\u003e(World Scientific, Singapore), and \u003ci\u003eCalculus of One Variable \u003c\/i\u003e(Ane Books Pvt. Ltd, New Delhi), and he is also co-author of \u003ci\u003eLinear Algebra \u003c\/i\u003e(Springer, New York). \u003c\/p\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Default Title","offer_id":45600593608942,"sku":"9780367348397","price":155.55,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0630\/9612\/7726\/files\/9780367348397.jpg?v=1721474471","url":"https:\/\/bookland.com.au\/products\/measure-and-integration-hardback","provider":"Book Land AU","version":"1.0","type":"link"}