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{{r|Measure theory}}

{{r|Measure theory}}

...ical analysis]] and [[probability theory]], and is the basic concept of '''measure theory''', which studies the properties of [[sigma algebra|&sigma;-algebras]], mea The study of [[von Neumann algebra]]s is often called ''non-commutative measure theory'', as commutative von Neumann algebras are isomorphic to [[Lp space|L<sup>�

{{r|Measure theory}}

*[[Measure theory]]

In the ordinary [[axiomatization]] of [[probability theory]] by means of [[measure theory]], the problem is to construct a [[sigma-algebra]] of [[measurable set|meas In measure theory, if we have a [[countably infinite]] collection of measurable sets, then th

...and angles while retaining volumes (of geometric bodies) one moves toward measure theory. Besides the volume, a measure generalizes area, length, mass (or charge) d ...o volume (an example: the set of all rational points inside a given cube). Measure theory succeeded in extending the notion of volume (or another measure) to a vast

the (cumulative) [[distribution function (measure theory)|distribution function]], defined as <math> F(y) := P (X \le y) </math>,

*[[Measure theory]]

*[[Measure theory]]

...ibution|discrete probabilities]], [[probability density function]]s, and [[measure theory]]. Conditioning leads to a non-random result if the condition is completely ==Conditioning on the level of measure theory==

...ools of choice that were introduced in this effort in the 1960s and 1970s (measure theory and non-standard analysis) -- were substantially more complex than the tool ....edu/top/prin/txt/Comp/PC2.html '''Perfect Competition''']</ref> brought ''measure theory'' <ref name=MEASURETHEORY>[http://econpapers.repec.org/bookchap/eeemathes/