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MATHEMATICAL PRELIMINARIES

Eduard Feireisl

in Dynamics of Viscous Compressible Fluids

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528388
eISBN:
9780191713590
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528388.003.0002
Subject:
Mathematics, Applied Mathematics

The basic mathematical concepts used in the book are presumed in this chapter. The necessary function spaces framework — Lebesgue spaces, Sobolev spaces, and spaces of continuous functions — are ... More


Weak Convergence of Distributions

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0022
Subject:
Economics and Finance, Econometrics

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved, and the chapter then considers the ... More


Weak Convergence in Metric Spaces

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0026
Subject:
Economics and Finance, Econometrics

This chapter lays the foundations for functional limit theory by considering the case of general metric spaces, from a topological standpoint. It develops tools to replace the method of ... More


SEGMENTATION PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0006
Subject:
Mathematics, Applied Mathematics

The study of segmentation problems, i.e., variational problems where the unknown is a piecewise-constant function, allows the introduction of a new type of weak convergence, related to the weak* ... More


Weak Convergence in a Function Space

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0027
Subject:
Economics and Finance, Econometrics

This chapter applies the theory of Ch. 26 to the case of the space C of continuous functions on the unit interval. It is shown how to assign probability measures to C, and Weiner measure (Brownian ... More


Stochastic Processes

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0012
Subject:
Economics and Finance, Econometrics

This chapter begins with some fundamental ideas concerning random sequences, and related convergence concepts. It discusses the underlying probability model, and develops the idea of infinite ... More


Cadlag Functions

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0028
Subject:
Economics and Finance, Econometrics

This chapter considers the space D, of functions on the unit interval that are continuous on the right with left limits. D contains and extends the space C, but is nonseparable, so to work with it ... More


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