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...

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

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

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

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...

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

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

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

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...

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

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"...

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...

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...

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

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

all other known rocky bodies) so that their heat loss is minimal. Compactness measure of a shape Dust explosion Square–cube law Specific surface area Schmidt-Nielsen...

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

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

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...

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...

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

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...

outcome, while the intermediary measure of state-level majorities is rendered obsolete. Some opponents of the compact contend that it would lead to a...

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

descriptions as a fallback Haar measure – Left-invariant (or right-invariant) measure on locally compact topological group Lebesgue measure – Concept of area in...

greatest possible density. If K1,...,Kn are measurable subsets of a compact measure space X and their interiors pairwise do not intersect, then the collection...

\varepsilon >0} , there is a compact subset K ε {\displaystyle K_{\varepsilon }} of X {\displaystyle X} such that, for all measures μ ∈ M {\displaystyle \mu...

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...