==Example applications==
''MarketMarketNIGGRRProbability measures'' which assign probabilities to [[financial market]] spaces based on actual market movements are examplesalso of probability measures which are of interestused in [[mathematical finance]], e.g. in the pricing of [[financial derivativebiology]]s.<ref>''QuantitativeMathematical methodsMethods in derivatives pricingBiology'' by DomingoJ. TavellaDavid 2002Logan, William R. Wolesensky 2009 ISBN 0471470394475258758 [http://books.google.com/books?id=dHIMulKy8dYC6GGyquH8kLcC&pg=PA11PA195 page 11195]</ref> For instance, ain comparative [[riskneutralsequence measureanalysis]] is a probability measure whichmay assumesbe thatdefined the current value of assets isfor the [[expectedlikelihood value]]that ofa thevariant futuremay payoffbe [[discounted]]permissible atfor thean [[riskfreeamino rateacid]]. If there is a unique probability measure that must be used to price assets in a market, then the market is called a [[complete market]]sequence.<ref>''IrreversibleDiscovering decisionsbiomolecular undermechanisms uncertaintywith computational biology'' by SvetlanaFrank I.Eisenhaber Boyarchenko, Serge Levendorskiĭ 20072006 ISBN 30540387737453452762 [http://books.google.com/books?id=lpsrP5mQG_QCPygg7cIZTwIC&pg=PA11PA127 page 11127]</ref>
Not all measures that intuitively represent chance or likelihood are probability measures. For instance, although the fundamental concept of a system in [[statistical mechanics]] is a measure space, such measures are not always probability measures.<ref name=stern/> 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 [[congruence relationunder congruence]], although it may do so in the case of systems with just one degree of freedom.<ref name=gut/>
Probability measures are also used in [[mathematical biology]].<ref>''Mathematical Methods in Biology'' by J. David Logan, William R. Wolesensky 2009 ISBN 0470525878 [http://books.google.com/books?id=6GGyquH8kLcC&pg=PA195 page 195]</ref> For instance, in comparative [[sequence analysis]] a probability measure may be defined for the likelihood that a variant may be permissible for an [[amino acid]] in a sequence.<ref>''Discovering biomolecular mechanisms with computational biology'' by Frank Eisenhaber 2006 ISBN 0387345272 [http://books.google.com/books?id=Pygg7cIZTwIC&pg=PA127 page 127]</ref>
==See also==
