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

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

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

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

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...

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...

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...

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...

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

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

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

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

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...

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

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...

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

of test procedures.: 283  The above standards were chosen as they are universally available references and suited to the key application for which computed...

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...

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...

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...

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...

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...

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...

frequencies that allowed reasonably accurate pulse envelopes while still having measurable waveforms within the pulses, as well as developing displays capable of...

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

researched of all standardized nursing languages. For each problem a measurable goal/outcome is set. For each goal/outcome, the nurse selects nursing interventions...

qualitative characteristics of the concept may not be quantifiable or measurable at all, at least not directly. The temptation exists to ignore them, or...