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If {f_n} is a sequence of measurable functions, with 0<=f_n<=f_(n+1) for every n, then intlim_(n->infty)f_ndmu=lim_(n->infty)intf_ndmu.

Functions which have derivatives of all orders at all points and which, together with their derivatives, fall off at least as rapidly as |x|^(-n) as |x|->infty, no matter how ...

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).

For s_1,s_2=+/-1, lim_(epsilon_1->0; epsilon_2->0)1/(x_1-is_1epsilon_1)1/(x_2-is_2epsilon_2) =[PV(1/(x_1))+ipis_1delta(x_1)][PV(1/(x_2))+ipis_2delta(x_2)] ...

In analysis, the phrase "Riesz-Fischer theorem" is used to describe a number of results concerning the convergence of Cauchy sequences in L-p spaces. The theorem is named for ...

The word "spectrum" confusingly has a number of unrelated meanings in various branches of mathematics.

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

The first practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1x_1+a_2x_2+...+a_nx_n=0, or else establish bounds within ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...