Robert A. Wijsman Invariant measures on groups and their use in statistics (Hayward, CA: Institute of Mathematical Statistics, 1990)

Invariant measures on groups and their use in statistics

Robert A. Wijsman

Lecture Notes--Monograph Series, Volume 14
Hayward, CA: Institute of Mathematical Statistics, 1990.
238 pp.

Subjects:

62A05 (primary)
22D99 (secondary)
28C10 (secondary)
62H15 (secondary)

Permanent link to this monograph: http://projecteuclid.org/euclid.lnms/1215540653
Mathmatical Reviews number (MathSciNet): MR1218397
ISBN:0-940600-19-6

Miscellaneous Frontmatter

i-vi

Preface

vii-viii

1. Introduction

1-11

2. Spaces, Functions, and Groups Acting on Spaces

12-37

3. Differentiable Manifolds, Tangent Spaces, and Vector Fields

38-52

4. Differential Forms on Manifolds

53-66

5. Lie Groups and Lie Algebras

67-97

6. Integration on Locally Compact Spaces According to Bourbaki

98-118

7. Invariant and Relatively Invariant Measures on Locally Compact Groups and Spaces

119-150

8. Factorization of Measures on Locally Compact Spaces Induced by the Actions of a Group, with Help of a Global Cross Section: Theory

151-161

9. Application to Type I Problems: Special Group Structure

162-171

10. Application to Type II Problems: No Special Group Structure, But Global Cross Section Exists

172-181

11. Type II Problems: Global Slice

182-190

12. Comparison of Two Factorization Methods: Cross Section Versus Proper Action

191-197

13. Density Ratio of a Maximal Invariant

198-212

References

213-218

List of Symbols

219-224

Subject Index

225-238

Invariant measures on groups and their use in statistics

Subjects:

Institute of Mathematical Statistics Lecture Notes - Monograph Series