Selected Problems in Real Analysis

[1055/94%]

B. M. Makarov, M. G. Goluzina, A. A. Lodkin, A. N. Podkorytov

Chapter IIntroduction[107/91%]

Section I.1Sets[41/93%]

Section I.2Inequalities[41/85%]

Section I.3Irrationality[25/96%]

Chapter IISequences[64/95%]

Section II.1Computing Limits[28/93%]

Section II.2Averaging of Sequences[19/95%]

Section II.3Recurrent Sequences[17/100%]

Chapter IIIFunctions[95/91%]

Section III.1Continuity and Discontinuities of Functions[28/100%]

Section III.2Semicontinuous Functions[6/33%]

Section III.3Continuous and Differentiable Functions[32/84%]

Section III.4Continuous Mappings[8/100%]

Section III.5Functional Equations[21/100%]

Chapter IVSeries[119/99%]

Section IV.1Convergence[10/100%]

Section IV.2Properties of Numerical Series Related to Monotonicity[23/100%]

Section IV.3Various Statements about Series[20/100%]

Section IV.4Computing Sums of Series[21/100%]

Section IV.5Functional Series[21/100%]

Section IV.6Trigonometric Series[24/96%]

Chapter VThe Integral[66/100%]

Section V.1Improper Integrals of Functions of One Variable[47/100%]

Section V.2Computing Multiple Integrals[19/100%]

Chapter VIAsymptotics[110/93%]

Section VI.1Asymptotics of Integrals[27/96%]

Section VI.2Laplace's Method[23/100%]

Section VI.3Asymptotics of Sums[41/88%]

Section VI.4Asymptotics of Implicit Functions and Recurrent Sequences[19/89%]

Chapter VIIFunctions (continued)[118/96%]

Section VII.1Convexity[41/98%]

Section VII.2Smooth Functions[27/93%]

Section VII.3Bernstein Polynomials[23/100%]

Section VII.4Almost Periodic Functions and Sequences[27/93%]

Chapter VIIILebesgue Measure and Integral[173/95%]

Section VIII.1Lebesgue Measure[30/97%]

Section VIII.2Measurable Functions[18/100%]

Section VIII.3Summable Functions[47/87%]

Section VIII.4The Stieltjes Integral[14/93%]

Section VIII.5ε-Entropy and Hausdorff Measures[32/97%]

Section VIII.6Asymptotics of High-Multiplicity Integrals[32/100%]

Chapter IXSequences of Measurable Functions[124/92%]

Section IX.1Convergence in Measure and Almost Everywhere[16/81%]

Section IX.2Convergence in the Mean. The Law of Large Numbers[20/90%]

Section IX.3Rademacher Functions. The Khinchin Inequality[31/90%]

Section IX.4Fourier Series and Transform[57/96%]

Chapter XIterations of Interval Transformations[79/94%]

Section X.1Topological Dynamics[43/88%]

Section X.2Measure-Preserving Transformations[36/100%]