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The Minkowski measure of a bounded, closed set is the same as its Lebesgue measure.

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

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 ...

The standard Gauss measure of a finite dimensional real Hilbert space H with norm ||·||_H has the Borel measure mu_H(dh)=(sqrt(2pi))^(-dim(H))exp(1/2||h||_H^2)lambda_H(dh), ...

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...

A Radon measure is a Borel measure that is finite on compact sets.

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...