Dynkin system [SEP] named after
Dynkin system
A Dynkin system, named after Eugene Dynkin, is a collection of subsets of another universal set formula_1 satisfying a set of axioms weaker than those of σ-algebra. Dynkin systems are sometimes referred to as λ-systems (Dynkin himself used this term) or d-system. These set families have applications in measure theory and probability.
A major application of λ-systems is the π-λ theorem, see below.
Definitions.
Let Ω be a nonempty set, and let formula_2
Coxeter notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more comprehensively defined by Norman Johnson.
Reflectional groups.
For Coxeter groups, defined by pure reflections, there is a direct correspondence between the bracket notation and Coxeter-Dynkin diagram