measure of set
121There is no infinite-dimensional Lebesgue measure — In mathematics, it is a theorem that there is no analogue of Lebesgue measure on an infinite dimensional space. This fact forces mathematicians studying measure theory on infinite dimensional spaces to use other kinds of measures: often, the… …
122Quasi-invariant measure — In mathematics, a quasi invariant measure mu; with respect to a transformation T , from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function by T . An important class of examples occurs when X… …
123Nikodym set — In mathematics, a Nikodym set is the seemingly paradoxical result of a construction in measure theory. A Nikodym set in the unit square S in the Euclidean plane E2 is a subset N of S such that the area (i.e. two dimensional Lebesgue measure) of N …
124Product measure — In mathematics, given two measurable spaces and measures on them, one can obtain the product measurable space and the product measure on that space. Conceptually, this is similar to defining the Cartesian product of sets and the product topology… …
125Singular measure — In mathematics, two positive (or signed or complex) measures μ and ν defined on a measurable space (Ω, Σ) are called singular if there exist two disjoint sets A and B in Σ whose union is Ω such that μ is zero on all measurable subsets of B while… …
126Empirical measure — In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise definition is found below. Empirical measures are relevant to mathematical… …
127Chinese measure word — In the modern Chinese languages, measure words or classifiers (zh tsp|t=量詞|s=量词|p=liàngcí; Cantonese (Yale): leung4 chi4 ) are used along with numerals to define the quantity of a given object or objects, or with this / that to identify specific… …
128Porous set — In mathematics, a porosity is a concept in the study of metric spaces. Like the concepts of meagre and measure zero sets, porosity is a notion of a set being somehow sparse or lacking bulk ; however, porosity is not equivalent to either of the… …
