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For any two ergodic measure-preserving transformations on nonatomic probability spaces, there is an isomorphism between the two probability spaces carrying orbits onto orbits.

If x is a member of a set A, then x is said to be an element of A, written x in A. If x is not an element of A, this is written x not in A. The term element also refers to a ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

A morphism f:Y->X in a category is an epimorphism if, for any two morphisms u,v:X->Z, uf=vf implies u=v. In the categories of sets, groups, modules, etc., an epimorphism is ...

A more common way to describe a Euclidean ring.

A system of congruences a_i mod n_i with 1<=i<=k is called a complete residue system (or covering system) if every integer y satisfies y=a_i (mod n) for at least one value of ...

Exotic cohomology is a cohomology theory that extends index theory to a larger class of manifolds.

The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

A game in which each player has a finite number of moves and a finite number of choices at each move.

The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group H, denoted F(H). In the case of a finite group, the subgroup generated will itself ...