disjoint balls
1Packing dimension — In mathematics, the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension is in some sense dual to Hausdorff dimension, since packing dimension is constructed by …
2Minkowski–Bouligand dimension — Estimating the box counting dimension of the coast of Great Britain In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box counting dimension, is a way of determining the fractal dimension of a set S in a …
3Minkowski-Bouligand dimension — In fractal geometry, the Minkowski Bouligand dimension, also known as Minkowski dimension or box counting dimension, is a way of determining the fractal dimension of a set S in a Euclidean space R^n, or more generally in a metric space ( X , d ) …
4Manifold decomposition — In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M. Manifold… …
5Besicovitch covering theorem — In mathematical analysis, a Besicovitch cover is an open cover of a subset E of the Euclidean space R N by balls such that each point of E is the center of some ball in the cover.The Besicovitch covering theorem asserts that there exists a… …
6Peetre theorem — In mathematics, the (linear) Peetre theorem is a result of functional analysis that gives a characterisation of differential operators in terms of their effect on generalized function spaces, and without mentioning differentiation in explicit… …
7Covering number — Not to be confused with Winding number or degree of a continuous mapping, sometimes called covering number or engulfing number . In mathematics, the ε covering number of a metric space (X, d), for some ε > 0, is the minimum… …
8Dimension function — In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple diameter to the dimension… …
9Vitali covering lemma — In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. tatement of the lemma* Finite version: Let B {1},...,B {n} be any collection of d dimensional balls contained… …
10probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …
