Preface
Bibliography
Acknowledgments
1 Introduction to Rn
A Sets
B Countable Sets
C Topology
D Compact Sets
E Continuity
F The Distance Function
2 Lebesgue Measure on Rn
A Construction
B Properties of Lebesgue Measure
C Appendix: Proof of P1 and P2
3 Invariance of Lebesgue Measure
A Some Linear Algebra
B Translation and Dilation
C Orthogonal Matrices
D The General Matrix
4 Some Interesting Sets
A A Nonmeasurable Set
B A Bevy of Cantor Sets
C The Lebesgue Function
D Appendix: The Modulus of Continuity
of the Lebesgue Functions
5 Algebras of Sets and Measurable Functions
A Algebras and a-Algebras
B Borel Sets
C A Measurable Set which Is Not a Borel Set
D Measurable Functions
E Simple Functions
6 Integration
A Nonnegative Functions
B General Measurable Functions
C Almost Everywhere
D Integration Over Subsets of Rn
E Generalization: Measure Spaces
F Some Calculations
G Miscellany
7 Lebesgue Integral on n
A Riemann Integral
B Linear Change of Variables
C Approximation of Functions in L1
D Continuity of Translation in L1
8 Fubini's Theorem for Rn
9 The Gamma Function
A Definition and Simple Properties
B Generalization
C The Measure of Balls
D Further Properties of the Gamma Function