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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 ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

Let mu be a positive measure on a sigma-algebra M, and let lambda be an arbitrary (real or complex) measure on M. If there is a set A in M such that lambda(E)=lambda(A ...

The Royle graphs are the two unique simple graphs on eight nodes whose sigma polynomials have nonreal roots (Read and Wilson 1998, p. 265). The sigma polynomials of these ...

The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

The q-analog of integration is given by int_0^1f(x)d(q,x)=(1-q)sum_(i=0)^inftyf(q^i)q^i, (1) which reduces to int_0^1f(x)dx (2) in the case q->1^- (Andrews 1986 p. 10). ...

A flow line for a map on a vector field F is a path sigma(t) such that sigma^'(t)=F(sigma(t)).

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...