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Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

A sigma-algebra which is related to the topology of a set. The Borel sigma-algebra is defined to be the sigma-algebra generated by the open sets (or equivalently, by the ...

A set equipped with a sigma-algebra of subsets.

The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

A distribution which arises in the study of integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)-1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)-1) = ...

An occurrence of a variable in a logic which is not free. Bound variables are also called dummy variables.

The set of points, known as boundary points, which are members of the set closure of a given set S and the set closure of its complement set. The boundary is sometimes called ...

Each of the maps in a chain complex ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... is known as a boundary operator.