Synopsis
Integration is one of the two cornerstones of analysis. In the fundamental work of Lebesgue, integration is presented in terms of measure theory. This introductory text starts with the historical development of the notion of set theory and integral theory. From here, the reader is naturally led to the consideration of the Lebesgue Integral, where abstract integration is developed via the measure theory. The important topics like the Outer Measure, Cantor's Ternary Set, Measurable Function, the Lebesgue Integral, Fundamental Theorem of Calculus, Lp-spaces, Fubini's Theorem, the Radon-Nikodym Theorem, and so on are discussed. The text is written in an informal style to make the subject matter easily comprehensible. Concepts have been developed with the help of motivating examples and probing questions, followed by numerous exercises. The book is suitable both as a textbook for an introductory course on the topic or for self-study. The core material is interspersed with examples, theorems, recapitulations, multiple choice questions, true/false questions and fill-in-the-blanks questions after relevant discussions of the topics.
About the Author
A K Malik, Faculty of Mathematics, B.K. Birla Institute of Engineering & Technology, Pilani (Rajasthan), has experience of more than six years in academics and research. His area of specialization is Inventory and Supply Chain Management. He has published more than twenty research papers in reputed national and international journals and is member of various committees. He has attended many seminars/conferences and presented his research papers. He is editorial board member of International Journal of Soft Computing and Engineering; International Journal of Mathematical Science; International Journal of Mathematical Sciences and Applications and American Journal of Mathematics and Sciences. He is author/co-author of six books.
S.C. Malik, is presently working as Professor in the Department of Statistics, M.D. University, Rohtak, Haryana. Apart from authoring a number of books he has presented the papers/talks in India and abroad including the USA, the UK, Portugal, Singapore, Germany, France, Belgium and Switzerland. He is the founder President of Indian Association for Reliability and Statistics (IARS). He has recently elected as member of the section of Mathematical Sciences of ISCA.
S.K. Gupta, Associate Professor of Mathematics, D.N. College, Meerut, Uttar Pradesh, India, has more than twenty years of experience in academics and research work. He has authored several books for U.G. and P.G. students of Indian universities. He is an active member of Ramanujan Mathematical Society.
S.R. Singh, Associate Professor of Department of Mathematics at CCS University Meerut, Uttar Pradesh, India, has lot of published work. He was awarded Swarn Jayanti Puraskar for best research paper at national academy of sciences. He is the President of the Operational Research Society of India, Meerut Chapter.
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