• < f is increasing. The latter part of the book deals with functions of bounded variation and approximately continuous functions. Finally there is an exhaustive chapter on the generalized Cantor sets and Cantor functions. The bibliography is extensive and a great variety of exercises serves to clarify and sometimes extend the results presented in the text.

Autorentext

R. Kannan is an Honorary Professor of Madras School of Economics. He retired as Principal Advisor at the Reserve Bank of India after 30 years of service. While at the RBI, he was deputed to the IMF as an advisor (1996-2001) and was also an advisor to the Governor of the Bank of Mauritius (1994-96). He was member of the Insurance Regulatory and Development Authority, and was closely involved in writing the BASEL III regulations of selected Asian economies. He has published about 50 papers in various journals encompassing monetary policy, fiscal policy, balance of payments, exchange rate, pensions, economic capital for the life insurance industry, and early warning systems for the life insurance industry. He is currently teaching at the MSE on risk measurement and management, central banking, financial regulations and banking supervision. K.R. Shanmugam is a Professor and the Director of Madras School of Economics, specialising in applied economics, public finance, finance and banking. He is also a non-official independent director of ITI limited, a member of the Steering Committee on Research in Environment at the MoEFCC, and member of the Academic Council of the Central University of Tamil Nadu. He has published about 40 research articles in various journals and edited volumes, and has edited five books. Saumitra Bhaduri received his Master's degree in Econometrics from Calcutta University, Kolkata, India, and his PhD in Financial Economics from Indira Gandhi Institute of Development Research (IGIDR), Mumbai, India. He currently works as a Professor at Madras School of Economics, Chennai, India, where he regularly offers courses on financial economics and econometrics, and on advanced quantitative techniques. He previously worked at GE Capital, the financial services division of the General Electric Company, and has held various quantitative analysis positions in the company's finance services. He alsofounded and headed the GE - MSE Decision Sciences Laboratory, where he was responsible for developing state-of-the-art research output for GE. He has also published several research articles in various international journals. His research interests include financial economics and econometrics, quantitative techniques and advanced analytics.

Inhalt
0 Preliminaries.- 0.1 Lebesgue Measure.- 0.2 The Lebesgue Integral.- 0.3 Vitali Covering Theorem.- 0.4 Baire Category Theorem and Baire Class Functions.- 1 Monotone Functions.- 1.1 Continuity Properties.- 1.2 Differentiability Properties.- 1.3 Reconstruction of f from f?.- 1.4 Series of Monotone Functions.- Exercises.- 2 Density and Approximate Continuity.- 2.1 Preliminaries and Definitions.- 2.2 The Lebesgue Density Theorem.- 2.3 Approximate Continuity.- 2.4 Approximate Continuity and Integrability.- 2.5 Further Results on Approximate Continuity.- 2.6 Sierpinski's Theorem.- 2.7 The Darboux Property and the Density Topology.- Exercises.- 3 Dini Derivatives.- 3.1 Preliminaries and Definitions.- 3.2 Simple Properties of Derivatives.- 3.3 Ruziewicz's Example.- 3.4 Further Properties of Derivatives.- 3.5 The Denjoy-Saks-Young Theorem.- 3.6 Measurability of Dini Derivatives.- 3.7 Dini Derivatives and Convex Functions.- Exercises.- 4 Approximate Derivatives.- 4.1 Definitions.- 4.2 Measurability of Approximate Derivatives.- 4.3 Analogue of the Denjoy-Saks-Young Theorem.- 4.4 Category Results for Approximate Derivatives.- 4.5 Other Properties of Approximate Derivatives.- Exercises.- 5 Additional Results on Derivatives.- 5.1 Derivatives.- 5.2 Derivates.- 5.3 Approximate Derivatives.- 5.4 The Denjoy Property.- 5.5 Metrically Dense.- 6 Bounded Variation.- 6.1 Bounded Variation of Finite Intervals.- 6.2 Stieltjes Integral.- 6.3 The Space BV[a,b].- BVloc and L1loc.- 6.5 Additional Remarks on Fubini's Theorem.- Exercises.- 7 Absolute Continuity.- 7.1 Absolute Continuity.- 7.2 Rectifiable Curves.- Exercises.- 8 Cantor Sets and Singular Functions.- 8.1 The Cantor Ternary Set and Function.- 8.2 Hausdorff Measure.- 8.3 Generalized Cantor SetsPart I.- 8.4 Generalized CantorSetsPart II.- 8.5 Cantor-like Sets.- 8.6 Strictly Increasing Singular Functions.- Exercises.- 9 Spaces of BV and AC Functions.- 9.1 Convergence in Variation.- 9.2 Convergence in Length.- 9.3 Norms on AC.- 9.4 Norms on BV.- 10 Metric Separability.- Exercises.