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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 set of points capable of being enclosed in intervals whose total length is arbitrarily small.

A Boolean sigma-algebra which possesses a measure.

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

A measure for which the q-dimension D_q varies with q.

mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

If mu is a real measure (i.e., a measure that takes on real values), then one can decompose it according to where it is positive and negative. The positive variation is ...