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If mu is a real measure (i.e., a measure that takes on real values), then one can decompose it according to where it is positive and negative. The positive variation is ...

With a large enough sample, any outrageous thing is likely to happen (Diaconis and Mosteller 1989). Littlewood (1986) considered an event which occurs one in a million times ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...

A polar representation of a complex measure mu is analogous to the polar representation of a complex number as z=re^(itheta), where r=|z|, dmu=e^(itheta)d|mu|. (1) The analog ...

Let X be a normed space and X^(**)=(X^*)^* denote the second dual vector space of X. The canonical map x|->x^^ defined by x^^(f)=f(x),f in X^* gives an isometric linear ...

Two complex measures mu and nu on a measure space X, are mutually singular if they are supported on different subsets. More precisely, X=A union B where A and B are two ...

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

An analytic function f(z) satisfying the irreducible algebraic equation A_0(z)f^k+A_1(z)f^(k-1)+...+A_k(z)=0 with single-valued meromorphic functions A_j(z) in a complex ...

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...