Synopsis
The book is intended to serve as a textbook for a course on Measure and Integration, for the graduate and M Phil level students at various Universities. It can be equally useful as a reference book for those who are involved in research in areas requiring the Lebesgue Theory of Integration in its generality. Pains have been taken to give detailed explanations of reasons of work and of the method used. Details are explicitly presented keeping the interest of students in view. The material has been arranged by sections, spread out in eleven chapters. The text starts with a chapter on preliminaries discussing basic concepts and results which would be taken for granted later. This is followed by chapters on Lebesgue Measurable Sets, Measure Spaces, Measurable Functions, Integration, Signed Measures, The Spaces Lp , Product Measure Spaces and Lebesgue-Stieltjes Integral.
About the Author
Pawan Kumar Jain (b. 1942) Fellow of the National Academy of Sciences (FNA Sc); formerly, Professor and Head, Department of Mathematics, University of Delhi and Emeritus Fellow of the UGC; and having teaching and research experience of 43 years, has published 130 research papers and 12 expository articles in areas of Complex Analysis, Functional Analysis, Sobolev Spaces, Hardy-type Inequalities and Operators, Theory of Frames; supervised 24 PhDs and 27 MPhils; published seven textbooks and edited twelve volumes. He has travelled widely in India and abroad for academic activities; besides his visits to USA, Canada, Germany, Kuwait, Sudan, Tanzania, Iran, Hong Kong, Jordan, China, Pakistan. He was nominated by the Indian National Science Academy to visit U.K. for three weeks during 2000-01 under the Exchange of Scientists Programme between INSA and Royal Society of London. He was awarded Visiting Professorship at Yarmouk University under the Joint Professorship Programme in Science and Sustainable Development of ISCU/TWAS/UNESCO/CSE/ Earth Council for a period of five years (1996-01). By now he has delivered several invited talks/colloquium lectures in India and abroad including the lectures at the University of Sussex, Imperial College of London and University of Oxford in UK; Auburn University, Tuskegee University and Clemson University in USA; McMaster University in Canada, Chinese University of Hong Kong. He was a member on the Curriculum Development Committee in Mathematics appointed by the UGC to frame syllabi at UG and PG levels. He has worked on several academic bodies/committees of UGC, DST, CSIR, MHRD, etc. Pankaj Jain (b. 1964) PhD&-Associate Professor of Mathematics at South Asian University, New Delhi (A University established by SAARC Nations). A specialist of analysis, in his 23 years of teaching experience so far, Dr. Jain has taught several courses of pure and applied mathematics both at undergraduate as well as at post graduate level. He has supervised 7 PhD students and has authored 40 research papers in various International journals with his students and other associates including 7 from outside India (Italy, Norway, Sweden and UK). Dr. Jain has received grants from various agencies in India and abroad in connection with research projects, attending International Conferences and collaborating with foreign mathematicians. This includes BOYSCAST fellowship of DST visiting Sweden and Exchange Program of Royal Society (London) visiting UK three times.
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