Compactness measure is a numerical quantity representing the degree to which a shape is compact. The circle and the sphere are the most compact planar...

analysis, two measures of non-compactness are commonly used; these associate numbers to sets in such a way that compact sets all get the measure 0, and other...

The Polsby–Popper test is a mathematical compactness measure of a shape developed to quantify the degree of gerrymandering of political districts. The...

roundness A circularity ratio as a compactness measure of a shape An assumption of ANOVAs, with repeated-measures, often called "sphericity" Circular...

Compactness can refer to: Compact space, in topology Compact operator, in functional analysis Compactness theorem, in first-order logic Compactness measure...

In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral...

finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible"...

can turn without failing. Sphericity is a specific example of a compactness measure of a shape. Sphericity applies in three dimensions; its analogue...

topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space...

analysis: Shape factor (image analysis and microscopy) including: The compactness measure of a shape In statistics: The shape parameter, sometimes referred...

starting point and should be built upon with additional measures, like the compactness measure of a shape to prevent against gerrymandering. Citing in...

In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures...

include: Borel measure, Jordan measure, ergodic measure, Gaussian measure, Baire measure, Radon measure, Young measure, and Loeb measure. In physics an...

homeomorphism) locally compact Hausdorff space X. This is shown using the Gelfand representation. The notion of local compactness is important in the study...

circle and goes down as far as 0 for highly non-circular shapes. Compactness measure of a shape Eccentricity (mathematics), how much a conic section (e...

medical professionals, the Pageboy was considered "cutting edge and compact", measuring 5.25 inches by 2.36 inches. In 1967, low-frequency Pageboys operating...

property of local compactness, and as such motivated the search for the more general theory, presented here. Any discrete group is locally compact. The theory...

Radon–Nikodym derivative, or density, of a measure. We have the following chains of inclusions for functions over a compact subset of the real line: absolutely...

sets and from below by compact measurable sets. Let (X, T) be a topological space and let Σ be a σ-algebra on X. Let μ be a measure on (X, Σ). A measurable...

American political scientist Polsby–Popper test, a mathematical compactness measure This page lists people with the surname Polsby. If an internal link...

all other known rocky bodies) so that their heat loss is minimal. Compactness measure of a shape Dust explosion On Being the Right Size Square–cube law...

counting measure is σ -finite. Locally compact groups which are σ-compact are σ-finite under the Haar measure. For example, all connected, locally compact groups...

functionals on spaces of continuous functions on a locally compact space to measures in measure theory. The theorem is named for Frigyes Riesz (1909) who...

Baire measure is a measure on the σ-algebra of Baire sets of a topological space whose value on every compact Baire set is finite. In compact metric...

require additional restrictions on the measure, as described below. Let X {\displaystyle X} be a locally compact Hausdorff space, and let B ( X ) {\displaystyle...

In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a...

α , {\textstyle \bigcup U_{\alpha },} a simple argument based on the compactness of the support of ϕ {\displaystyle \phi } and a partition of unity shows...

with the Haar measure introduced by John von Neumann, André Weil and others depends on the theory of the dual group of a locally compact abelian group...

boundary has Lebesgue measure zero. (Or equivalently, if the boundary has Jordan measure zero; the equivalence holds due to compactness of the boundary.)...

patents, and prototypes instigated and in some measure influenced the compact disc's design. The compact disc is an evolution of LaserDisc technology,...