# Real and complex analysis

@inproceedings{Rudin1966RealAC, title={Real and complex analysis}, author={Walter Rudin}, year={1966} }

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure…

## 6,197 Citations

### Elements of Functional Analysis

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This chapter is devoted to a review of standard topics from functional analysis such as quasinormed and normed linear spaces and closed, compact and Fredholm linear operators on Banach spaces. These…

### Approximation of Holomorphic Functions in the Complex Plane

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This thesis is a study of approximation of holomorphic functions, by polynomials, rational functions or entire functions. Hörmander's L existence theorem for the Cauchy-Riemann operator is proved and…

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### Linear Functional Analysis

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Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are…

### Spectral Measures In Abstract Spaces

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- 2007

We study the theory of spectral measures in topological vector spaces. We extend the Hilbert space theory to this setting and generalize the notion of spectral measures in some useful ways to provide…

### Helsinki lectures - May 2013 SPACES OF ANALYTIC FUNCTIONS, GEOMETRY OF DOMAINS, AND SUPERPOSITION OPERATORS

- Mathematics
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We review some relationships between the growth of univalent functions in classical spaces of analytic functions and the geometry of image domains under such maps and apply this to obtain the…

### The Birkhoff integral and the property of Bourgain

- Mathematics
- 2005

Abstract.In this paper we study the Birkhoff integral of functions f:Ω→X defined on a complete probability space (Ω,Σ,μ) with values in a Banach space X. We prove that if f is bounded then its…

### Extensions of Domain Maps in Differential and Integral Calculus

- Mathematics2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

It is proved that the subspace of real-valued continuously differentiable functions on a finite dimensional Euclidean space is dense in the space of Lipschitz maps equipped with the L-topology, and it is shown that the Lebesgue integral operator on integrable functions is the extension of the R-integral operator on continuous functions.

### Some degeneracy theorems for entire functions with values in an algebraic variety

- Mathematics
- 1972

In the first part of this paper we prove the following extension theorem. Let P* be a q-dimensional punctured polycylinder, i.e. a product of disks and punctured disks. Let Wn be a compact complex…

### Vector-valued holomorphic functions in several variables

- Mathematics
- 2020

In the present paper we give some explicit proofs for folklore theorems on holomorphic functions in several variables with values in a locally complete locally convex Hausdorff space $E$ over…