Schweizer B., Sklar A. Probabilistic Metric Spaces

New York: Dover Publications, 2005. — 230 p.Special Symbols
Beginnings
Menger,
Developments
Some Examples
Šerstnev,
Random Metric Spaces
Topologies
Tools
Postscript
Sets and Functions
Functions on Intervals
Probabilities, Integrals, Random Variables
Binary Operations
Metric and Related Spaces
Isometries, Homotheties, Metric Transforms
Betweenness
Topological Structures
Spaces of Distribution Functions
The Modified Lévy Metric
The Space of Distance Distribution Functions
Quasi-Inverses of Nondecreasing Functions
Associative Binary Operations
Generators and Ordinal Sums
Associative Functions on Intervals
Representation of Archimedean Functions
Triangular Norms, Additive and Multiplicative Generators
Examples
Conorms and Composition Laws
Open Problems
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
Open ProblemsThe Operations τT, L
The Operations τT*, L
The Operations σC, L
The Operations ρC, L
Derivability and Nonderivability from Functions of Random Variables
Duality
The Conjugate Transform
Open Problems
Probabilistic Metric Spaces in General
Transformed Triangle Inequalities and Derived Metrics
Simple Spaces
Ellipse m-Metrics and Hysteresis
α-Simple Spaces
Open Problems
E-Spaces
Pseudometrically Generated Spaces, Sherwood’s Theorem
Random Metric Spaces
The Probability of the Triangle Inequality
W-Spaces
Open ProblemsConsistency, Triangle Inequalities
C-Spaces
Homogeneous and Semihomogeneous C-Spaces
Moments and Metrics
Normal C-Spaces
Moments in Normal C-Spaces
Open Problems
Transformation-Generated Spaces
Measure-Preserving Transformations
Mixing Transformations
Recurrence
E-Processes: The Case of Markov Chains
Open Problems
The Strong Topology and Strong Uniformity
Uniform Continuity of the Distance Function
Examples
The Probabilistic Diameter
Completion of Probabilistic Metric Spaces
Contraction Maps
Product Spaces
Countable Products
The Probabilistic Hausdorff Distance
Discemibility Relations
Open Problems
Profile Closures
Distinguishability
Wald Betweenness
Menger Betweenness
Probabilistic Betweenness
Open Problems
Probabilistic Normed Spaces
Probabilistic Inner Product Spaces
Probabilistic Topologies
Probabilistic Information Spaces
Generalized Metric SpacesErrataSupplementary References