particular, a universally measurable set of reals is necessarily Lebesgue measurable (see § Finiteness condition below). Every analytic set is universally measurable...

{\mathcal {B}},} the projected set onto X {\displaystyle X} is a universally measurable set relatively to F . {\displaystyle {\mathcal {F}}.} An important...

dense set Bounded set Totally bounded set Borel set Baire set Measurable set, Non-measurable set Universally measurable set Negligible set Null set Haar...

Polish space Prewellordering Projective set Property of Baire Uniformization (set theory) Universally measurable set Determinacy AD+ Axiom of determinacy...

σ-algebra. The σ-algebra of Borel sets is the most popular, but not the only choice. (Baire sets, universally measurable sets, etc, are also used sometimes...

Polish space Prewellordering Projective set Property of Baire Uniformization (set theory) Universally measurable set Determinacy AD+ Axiom of determinacy...

Set of uniqueness Property of Baire Lebesgue measurable Universally measurable set Perfect set property Universally Baire set Meager set Comeager set...

on the universally measurable sets in C {\displaystyle C} such that a {\displaystyle a} is the barycenter of p , {\displaystyle p,} and the set of extreme...

theorem). Analytic sets are always Lebesgue measurable (indeed, universally measurable) and have the property of Baire and the perfect set property. When...

function selecting a member from each non-empty such Lebesgue-measurable subset. (The set B ( R ) {\displaystyle {\mathcal {B}}({\mathbb {R} })} is the...

theorem is that, given any measurable function g : Y → X {\displaystyle g:Y\to X} , there exists a universally measurable function f : g ( Y ) ⊂ X → Y...

PD implies that all projective sets are Lebesgue measurable (in fact, universally measurable) and have the perfect set property and the property of Baire...

of a set F is also known as the début of F. The Début theorem says that the hitting time of a measurable set F, for a progressively measurable process...

forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for...

Chervonenkis, 1968) Under certain consistency conditions, a universally measurable class of sets   C   {\displaystyle \ {\mathcal {C}}\ } is a uniform Glivenko-Cantelli...

laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantities but may be explained in terms of microscopic...

reals has the property of Baire, is Lebesgue measurable (in fact universally measurable) and has the perfect set property. The first periodicity theorem implies...

of reals in L(R) is Lebesgue measurable (in fact, universally measurable) and has the property of Baire and the perfect set property. L(R) does not satisfy...

and universally applicable the metric devised, the more complex and unemployable it becomes. A good metric must be clearly defined, simple, measurable, objective...

community as a whole that had misinterpreted von Neumann's proof as applying universally.) Bub provides evidence that von Neumann understood the limits of his...

is the example of a sample of gas contained in a container. The easily measurable parameters volume, pressure, and temperature of the gas describe its macroscopic...

relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally...

Cosets of Q in R are used in the construction of Vitali sets, a type of non-measurable set. Cosets are central in the definition of the transfer. Cosets...

was designed to set individual and collaborative goal team goals that are specific, concrete, challenging, ambitious and have measurable and time bound...

research, positive psychology lacked a common vocabulary for discussing measurable positive traits before 2004. Traditional psychology benefited from the...

Construct validity concerns how well a set of indicators represent or reflect a concept that is not directly measurable. Construct validation is the accumulation...

Company. pp. 15–16. Retrieved 2017-08-12. α = arcsin m This notation is universally used in Europe and is fast gaining ground in this country. A less desirable...

further that, as a result, there are almost no local effects, and only a measurable and widely agreed climate change effect, of a greenhouse gas emission...

upward. Numerical taxonomy is an approach based solely on observable, measurable similarities and differences of the things to be classified. Classification...

largely indescribable and unquantifiable through traditional means, yet measurable in the profound changes they have on the individuals that report such...