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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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