Foundations of real and abstract analysis

Real Analysis.- Analysis on the Real Line.- Differentiation and the Lebesgue Integral.- Abstract Analysis.- Analysis in Metric Spaces.- Analysis in Normed Linear Spaces.- Hilbert Spaces.- An Introduction to Functional Analysis.

[1]  Dudley,et al.  Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[2]  Robert Gray,et al.  Georg Cantor and Transcendental Numbers , 1994 .

[3]  N. Kalton SEQUENCES AND SERIES IN BANACH SPACES (Graduate Texts in Mathematics, 92) , 1985 .

[4]  K. Schittkowski,et al.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[5]  James H. Davenport,et al.  Integration in finite terms , 1984, SIGS.

[6]  J. Hennefeld A NONTOPOLOGICAL PROOF OF THE UNIFORM BOUNDEDNESS THEOREM , 1980 .

[7]  W. Pfaffenberger A Converse to a Completeness Theorem , 1980 .

[8]  Y. Wong The Lebesgue Covering Property and Uniform Continuity , 1972 .

[9]  R. Solovay A model of set-theory in which every set of reals is Lebesgue measurable* , 1970 .

[10]  John Todd,et al.  Introduction to the constructive theory of functions , 1965 .

[11]  Y. Matsuoka An Elementary Proof of the Formula \Sum ∞ k = 1 1/k 2 = π 2 /6 , 1961 .

[12]  Leon Henkin,et al.  Review: Kurt Godel, The Consistency of the Axiom of Choice and the Generalized Continuum-Hypothesis with the Axioms of Set Theory , 1952 .

[13]  N. S. Mendelsohn An Application of a Famous Inequality , 1951 .

[14]  E. Zermelo Beweis, daß jede Menge wohlgeordnet werden kann , 1904 .

[15]  F. Takens Measure and category , 1988 .

[16]  R. Kadison,et al.  Fundamentals of the Theory of Operator Algebras , 1983 .

[17]  M. Kline Mathematical Thought from Ancient to Modern Times , 1972 .

[18]  B. Szőkefalvi-Nagy Introduction to real functions and orthogonal expansions , 1965 .

[19]  B. L. Waerden Ein einfaches Beispiel einer nicht-differenzierbaren stetigen Funktion , 1930 .