Kuttler K. Real and Abstract Analysis

Brigham Young University, 2019. — 795 p.Topology, Continuity, And Algebra
Some Prerequisite Material.
Metric Spaces.
Normed Linear Spaces.
Brouwer Fixed Point Theorem in Rn.
Differentiation
The Derivative.
Implicit Function Theorem.
Integration
Abstract Measures And Measurable Functions.
The Lebesgue Integral In Rn.
Integration on Manifolds.
Divergence Theorem.
Line Integrals.
Green's And Stoke's Theorems.
Differential Forms.
The Lp Spaces.
Degree Theory, An Introduction.
The Integral And The Derivative In Rn
Integrals And Derivatives.
Differentiation Of Radon Measures.
Hausdorff Measure.
The Area Formula.
Abstract Theory
Hausdorff Spaces And Measures.
Product Measures.
Banach Spaces.
Hilbert Spaces.
Representation Theorems.
The Bochner Integral.
App. A Review Of Some Linear Algebra.
App. B The Hausdorff Maximal Theorem.
App. C Stone's Theorem And Partitions Of Unity.Last revision: 12.10.2019