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The Riemann's moduli space gives the solution to Riemann's moduli problem, which requires an analytic parameterization of the compact Riemann surfaces in a fixed ...

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...

One of the Eilenberg-Steenrod axioms. Let X be a single point space. H_n(X)=0 unless n=0, in which case H_0(X)=G where G are some groups. The H_0 are called the coefficients ...

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F]=dim_FK. If [K:F] is finite, ...

If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...

Lines that intersect in a point are called intersecting lines. Lines that do not intersect are called parallel lines in the plane, and either parallel or skew lines in ...