Research Catalog

Details

Additional authors

1. Sklar, A. (Abe)

Description

1. xvi, 275 p. : ill.; 24 cm.

Series statement

1. North Holland series in probability and applied mathematics

Uniform title

1. North Holland series in probability and applied mathematics

Subject

1. Metric spaces
2. Probabilities
3. Probability

Contents

1. Introduction and Historical Survey -- Menger, 1942 -- Wald, 1943 -- Developments, 1956-1960 -- Serstnev, 1962 -- Random Metric Spaces -- Topologies -- Tools -- Sets and Functions -- Functions on Intervals -- Probabilities, Integrals, Random Variables -- Binary Operations -- Metric and Topological Structures -- Metric and Related Spaces -- Isometries, Homotheties, Metric Transforms -- Betweenness -- Minkowski Metrics -- Topological Structures -- Distribution Functions -- Spaces of Distribution Functions -- The Modified Levy Metric -- The Space of Distance Distribution Functions -- Quasi-Inverses of Nondecreasing Functions -- Associativity -- Associative Binary Operations -- Generators and Ordinal Sums -- Associative Functions on Intervals -- Representation of Archimedean Functions -- Triangular Norms, Additive and Multiplicative Generators -- Conorms and Composition Laws -- Copulas -- Fundamental Properties of n-Increasing Functions -- Joint Distribution Functions, Subcopulas, and Copulas -- Copulas and t-Norms -- Dual Copulas -- Copulas and Random Variables -- Margins of Copulas -- Triangle Functions -- The Operations [tau subscript T,L] -- The Operations [tau subscript T*,L] -- The Operations [sigma subscript C,L] -- The Operations [rho subscript C,L] -- Derivability and Nonderivability from Functions of Random Variables -- Duality -- The Conjugate Transform -- Probabilistic Metric Spaces -- Probabilistic Metric Spaces in General -- Transformed Triangle Inequalities and Derived Metrics -- Equilateral Spaces.
2. Simple Spaces -- Ellipse m-Metrics and Hysteresis -- [alpha]-Simple Spaces -- Best-Possible Triangle Inequalities -- Random Metric Spaces -- E-Spaces -- Pseudometrically Generated Spaces, Sherwood's Theorem -- Random Metric Spaces -- The Probability of the Triangle Inequality -- W-Spaces -- Distribution-Generated Spaces -- Consistency, Triangle Inequalities -- C-Spaces -- Homogeneous and Semihomogeneous C-Spaces -- Moments and Metrics -- Normal C-Spaces -- Moments in Normal C-Spaces -- Transformation-Generated Spaces -- Transformation-Generated Spaces -- Measure-Preserving Transformations -- Mixing Transformations -- Recurrence -- E-Processes: The Case of Markov Chains -- The Strong Topology -- The Strong Topology and Strong Uniformity -- Uniform Continuity of the Distance Function -- The Probabilistic Diameter -- Completion of Probabilistic Metric Spaces -- Contraction Maps -- Product Spaces -- Countable Products -- The Probabilistic Hausdorff Distance -- Discernibility Relations -- Profile Functions -- Profile Closures -- Distinguishability -- Betweenness -- Wald Betweenness -- Transform Betweenness -- Menger Betweenness -- Probabilistic Betweenness -- Probabilistic Normed Spaces -- Probabilistic Inner Product Spaces -- Probabilistic Topologies -- Probabilistic Information Spaces -- Generalized Metric Spaces.

Owning institution

1. Harvard Library

Note

1. Includes index.

Bibliography (note)

1. Bibliography: p. [253]-266.

Processing action (note)

1. committed to retain