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On the Theory of Vector Measures
eBook ISBN:  9781470401566 
Product Code:  MEMO/12/195.E 
List Price:  $26.00 
MAA Member Price:  $23.40 
AMS Member Price:  $15.60 
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On the Theory of Vector Measures
eBook ISBN:  9781470401566 
Product Code:  MEMO/12/195.E 
List Price:  $26.00 
MAA Member Price:  $23.40 
AMS Member Price:  $15.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 12; 1977; 72 ppMSC: Primary 28

Table of Contents

Chapters

0. Background

1. Notation, definitions, and introduction

2. Boundedness in $S^\tau (\mathcal {R})$

3. $\beta (S^\tau (\mathcal {R})^*,S(\mathcal {R}))$ is the topology of the variation norm

4. Uniform strong boundedness and $\tau $equicontinuity

5. Buck’s $(\ell ^\infty , \beta )$ as an example of $\widehat {S^\tau (\mathcal {R})}$

6. An extension theorem

7. Every $\sigma $ideal determines a decomposition of $\operatorname {sca}(\mathcal {R},W)$

8. $\widehat {S^\tau (\mathcal {R})}$ as a projective limit

9. $\widehat {S^\tau (\mathcal {R}/\mu )}$ and the RadonNikodym theorem

10. Semireflexivity of $\widehat {S^\tau (\mathcal {R})}$ and the range of a vector measure

11. $\sigma (S^\tau (\mathcal {R})^*, \widehat {S^\tau (\mathcal {R})})$compactness, the BartleDunfordSchwartz theorem, and OrliczPettistype theorems

12. Applications to measure theory for (abstract) Boolean algebras


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Chapters

0. Background

1. Notation, definitions, and introduction

2. Boundedness in $S^\tau (\mathcal {R})$

3. $\beta (S^\tau (\mathcal {R})^*,S(\mathcal {R}))$ is the topology of the variation norm

4. Uniform strong boundedness and $\tau $equicontinuity

5. Buck’s $(\ell ^\infty , \beta )$ as an example of $\widehat {S^\tau (\mathcal {R})}$

6. An extension theorem

7. Every $\sigma $ideal determines a decomposition of $\operatorname {sca}(\mathcal {R},W)$

8. $\widehat {S^\tau (\mathcal {R})}$ as a projective limit

9. $\widehat {S^\tau (\mathcal {R}/\mu )}$ and the RadonNikodym theorem

10. Semireflexivity of $\widehat {S^\tau (\mathcal {R})}$ and the range of a vector measure

11. $\sigma (S^\tau (\mathcal {R})^*, \widehat {S^\tau (\mathcal {R})})$compactness, the BartleDunfordSchwartz theorem, and OrliczPettistype theorems

12. Applications to measure theory for (abstract) Boolean algebras
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