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Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

The normal bundle of a submanifold N in M is the vector bundle over N that consists of all pairs (x,v), where x is in N and v is a vector in the vector quotient space ...

The positive predictive value is the probability that a test gives a true result for a true statistic. The negative predictive value is the probability that a test gives a ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube I=[0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

The Machin-like formula 1/4pi=cot^(-1)2+cot^(-1)5+cot^(-1)8.

A generalization of spun knots due to Zeeman. This method produces four-dimensional knot types that cannot be produced by ordinary spinning.

The set of n quantities v_j are components of an n-dimensional vector v iff, under rotation, v_i^'=a_(ij)v_j (1) for i=1, 2, ..., n. The direction cosines between x_i^' and ...

The Machin-like formula 1/4pi=cot^(-1)(2)+cot^(-1)(3). The other 2-term Machin-like formulas are Hermann's formula, hutton's formula, and Machin's formula.

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. In this work, the term "constant" ...