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The book is intended to provide a basic course in Lebesgue Measure and Integration for the Honours and Postgraduate students of the various universities in India and abroad with the hope that it will open a path to the Lebesgue Theory to the students. Pains have been taken to give detailed explanations of reasons of work and of the method used together with numerous examples and counter examples at different places in this book. The details are explicitly presented keeping the interest of the students in view. Each topic, in the book, has been treated in an easy and lucid style. The material has been arranged by sections, spread out in seven chapters. The text opens with a chapter on preliminaries discussing basic concepts and results which would be taken for granted later in the book. The chapter is followed by chapters on Infinite Sets, Measurable Sets, Measurable Functions, Lebesgue Integral, Differentiation and Integration and the Lebesgue Lp-Spaces. The book contains many solved and unsolved problems, remarks and notes at places which would help the students in learning the course effectively.
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Pawan Kumar Jain (b. 1942) Fellow of the National Academy of Sciences (F.N.A.Sc); U.G.C. - Emeritus Fellow and formerly, Professor and Head, Department of Mathematics, University of Delhi, 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 Ph.Ds and 27 M.Phil.s; published six 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 and 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, NCERT etc.
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