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Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events; for example, the value assigned to the outcome "1 or 2" in a throw of a dice should be the sum of the
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is a measure space, such measures are not always probability measures. In general, in statistical physics, if we consider sentences of the form "the probability of a system S assuming state A is p" the geometry of the system does not always lead to the definition of a probability measure
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Not all measures that intuitively represent chance or likelihood are probability measures. For instance, although the fundamental concept of a system in
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of the future payoff taken with respect to that same risk neutral measure (i.e. calculated using the corresponding risk neutral density function), and
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750:{\displaystyle \mu \left(\bigcup _{i\in \mathbb {N} }E_{i}\right)=\sum _{i\in \mathbb {N} }\mu (E_{i}).}
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spaces based on actual market movements are examples of probability measures which are of interest in
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Dekking, Frederik Michel; Kraaikamp, Cornelis; Lopuhaä, Hendrik Paul; Meester, Ludolf Erwin (2005).
1201:-valued probability measures, allowing for many intuitive proofs based upon measures. For instance,
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a probability measure may be defined for the likelihood that a variant may be permissible for an
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Probability measures have applications in diverse fields, from physics to finance and biology.
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and the additive property is replaced by an order relation based on
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Probability measures are distinct from the more general notion of
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Measure of total value one, generalizing probability distributions
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in which there is no requirement that the fuzzy values sum up to
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For example, given three elements 1, 2 and 3 with probabilities
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1221: – Measure defined on all open sets of a topological space
1003:{\displaystyle \mu (B\mid A)={\frac {\mu (A\cap B)}{\mu (A)}}.}
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Discovering biomolecular mechanisms with computational biology
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Distinguishing probability measure, function and distribution
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satisfies the probability measure requirements so long as
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A course in mathematics for students of physics, Volume 2
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Pages displaying short descriptions of redirect targets
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Probability, Random
Processes, and Ergodic Properties
1304:"A Modern Introduction to Probability and Statistics"
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Svetlana I. Boyarchenko, Serge Levendorskiĭ 2007
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1280:An introduction to measure-theoretic probability
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1455:by J. David Logan, William R. Wolesensky 2009
392:values assigned to the outcomes "1" and "2".
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1151:Probability measures are also used in
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645:{\displaystyle E_{1},E_{2},\ldots }
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368:defined on a set of events in a
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1453:Mathematical Methods in Biology
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496:must return results in the
411:mapping the σ-algebra for
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1282:by George G. Roussas 2004
1582:Measures (measure theory)
1477:by Frank Eisenhaber 2006
1389:by Yair M. Guttmann 1999
1411:by Domingo Tavella 2002
1261:Probability distribution
287:Law of total probability
282:Conditional independence
171:Exponential distribution
156:Probability distribution
1506:Probability and Measure
1339:by Robert M. Gray 2009
1194:{\displaystyle \{0,1\}}
1032:{\displaystyle \mu (A)}
929:conditional probability
858:{\displaystyle \{1,3\}}
795:{\displaystyle 1/4,1/4}
446:The requirements for a
266:Conditional probability
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18:Measure (probability)
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1502:Billingsley, Patrick
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366:real-valued function
292:Law of large numbers
261:Marginal probability
186:Poisson distribution
35:Part of a series on
1561:Probability measure
1087:statistical physics
409:probability measure
376:properties such as
362:probability measure
251:Complementary event
193:Probability measure
181:Pareto distribution
176:Normal distribution
1527:. Academic Press.
1246:Martingale measure
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1116:. For instance, a
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44:Probability theory
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1203:Hindman's Theorem
1157:sequence analysis
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596:must satisfy the
567:{\displaystyle 1}
547:{\displaystyle 0}
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102:Probability space
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277:Independence
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358:mathematics
233:Random walk
74:Determinism
62:Probability
1571:Categories
1267:References
1161:amino acid
1126:discounted
534:returning
473:are that:
399:Definition
144:Experiment
91:Randomness
37:statistics
1324:1431-875X
1018:μ
983:μ
972:∩
963:μ
948:∣
939:μ
726:μ
716:∈
709:∑
680:∈
673:⋃
664:μ
640:…
604:countable
584:μ
484:μ
471:σ-algebra
457:μ
370:σ-algebra
137:Singleton
1504:(1995).
1486:page 127
1464:page 195
1398:page 149
1373:page 802
1348:page 163
1213:See also
1095:measures
218:Variance
1442:page 11
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1291:page 47
1128:at the
374:measure
132:Outcome
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67:Axioms
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364:is a
112:Event
1529:ISBN
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1341:ISBN
1320:ISSN
1284:ISBN
927:The
802:and
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