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The set of L^p-functions (where p>=1) generalizes L2-space. Instead of square integrable, the measurable function f must be p-integrable for f to be in L^p. On a measure ...

Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

"Much greater" is used to indicate a strong inequality in which a is not only greater than b, but much greater (by some convention), is denoted a>>b. For an astronomer, ...

A vector space V with a ring structure and a vector norm such that for all v,W in V, ||vw||<=||v||||w||. If V has a multiplicative identity 1, it is also required that ...

A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...