Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical … Wikipedia
Banach algebra — In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach… … Wikipedia
Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis … Wikipedia
Banach, Stefan — ▪ Polish mathematician born March 30, 1892, Kraków, Austria Hungary [now in Poland] died August 31, 1945, Lvov, Ukrainian S.S.R. [now Lviv, Ukraine] Polish mathematician who founded modern functional analysis and helped develop the theory… … Universalium
Measure of non-compactness — In functional 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 sets get measures that are bigger according to how far they are removed… … Wikipedia
Stefan Banach — Infobox Scientist name = Stefan Banach box width = image width = caption = birth date = Birth date|1892|3|30 birth place = death date = Death date|1945|8|31 death place = nationality = Polish citizenship = Austro Hungarian, Polish, Soviet Union [ … Wikipedia
Concentration of measure — In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that A random… … Wikipedia
Cylinder set measure — In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi measure, or CSM) is a kind of prototype for a measure on an infinite dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder … Wikipedia
Signed measure — In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values. Some authors may call it a charge,[1] by analogy with electric charge, which is a familiar distribution that takes on positive… … Wikipedia
There 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… … Wikipedia
