** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.

** Lebesgue covering dimension, a definition of dimension using topological properties

** Roman Britain or Britannia, a Roman province covering most of modern England and Wales and some of southern Scotland from 43 to 410 AD

** Freight Unit, which is currently developing the " London Freight Plan " and is involved with setting up and supporting a number of Freight Quality Partnerships covering key areas of London.

** A federal grand jury indicts Caspar Weinberger for his role in covering up the Iran – Contra affair.

** Species cirrostratus nebulosus ( Cs neb ): A featureless veil of high cloud covering the entire sky ( C < sub > H </ sub > 7 ).

** City of Adelaide, the South Australian local government area covering the city centre, North Adelaide and the parklands

** Electoral district of Albany, the district of the Western Australian Legislative Council covering Albany

** Roof shingle, a roof covering consisting of individual overlapping elements

** Chihuahuan Desert, a desert covering much of the state and adjacent regions

** Butt flap, a separately removable part of underwear ( un ) covering the buttocks

** 50, 000 watts covering 30 counties in Tennessee, Missouri, Kentucky, Arkansas since 1969

** 6, 000 watts covering 40-45 mile radius of 10 counties in Tennessee, Missouri, & Kentucky since June 2007

** 1, 000 watts covering Dyer County & Northwest Tennessee since 1959

** Burton ( UK Parliament constituency ), covering Burton upon Trent and surrounding areas

** City of Bunbury, the local government area covering Bunbury's central and southern suburbs

** General knowledge – covering the topics listed below ( if they are not in a separate round ) and also topics such as history, geography and science and nature.

** Demos / Demoi, the name for a specific type of subdivision or municipality in modern Greece ; an administrative area covering a city or several villages together

** Journal of the Optical Society of America A, 1984-present, covering research on optics, image science, and vision.

** Journal of the Optical Society of America B, 1984-present, covering research on optical physics

** Cuenca ( Spanish Congress Electoral District ), the electoral district covering the province

** Fu Rong, killed in action while covering the Shu army's retreat

** Fabric, simple covering without support

** group dynamics is useful in developing new streams of thought and covering an issue thoroughly

** A double covering group of a topological group such as a Lie group, a group extension of index two formed by a topological double cover.

** GSM / GPRS utilising 900MHz / 1800MHz covering 97 % of the population

** Satellite Telephony covering all of Australia.

** the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n.

** Minkowski – Bouligand dimension

** Spaces with integer dimension are better-behaved than spaces with fractal dimension.

** Hypersphere, a round sphere of dimension higher than 2, especially if embedded in such a space

** Krull dimension

** the unit sphere ( with superscript denoting dimension )

** Complex dimension

** Hausdorff dimension

** Inductive dimension

** Packing dimension

** Isoperimetric dimension

The Lebesgue covering dimension is defined as the minimum number of overlaps that small open balls need to have in order to completely cover the object.

* Lebesgue covering dimension

Menger showed, in the 1926 construction, that the sponge is a universal curve, in that any possible one-dimensional curve is homeomorphic to a subset of the Menger sponge, where here a curve means any compact metric space of Lebesgue covering dimension one ; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways.

Lebesgue covering dimension or topological dimension is one of several inequivalent notions of assigning a topological invariant dimension to a given topological space.

# redirect Lebesgue covering dimension

# redirect Lebesgue covering dimension

* Lebesgue covering dimension

* A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every open cover of the space has a refinement which is a cover of the space by open sets such that any point in the space is contained in exactly one open set of this refinement.

Brouwer, by use of the Lebesgue covering theorem ( a result based on compactness ).

# REDIRECT Lebesgue covering dimension # Properties

* Lebesgue covering dimension

# REDIRECT Lebesgue covering dimension