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Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

A quantity is said to be exact if it has a precise and well-defined value. J. W. Tukey remarked in 1962, "Far better an approximate answer to the right question, which is ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...

A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...