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035   $a(CKB)3710000000618943
035   $a(MiAaPQ)EBC4738785
035   $a(DE-B1597)467948
035   $a(OCoLC)979911355
035   $a(DE-B1597)9781400882144
035   $a(EXLCZ)993710000000618943
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aRadically Elementary Probability Theory. (AM-117), Volume 117 /$fEdward Nelson
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©2016
215   $a1 online resource (109 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v120
311   $a0-691-08474-2 
311   $a0-691-08473-4 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tTable of contents -- $tPreface -- $tAcknowledgments -- $t1. Random variables -- $t2. Algebras of random variables -- $t3. Stochastic processes -- $t4. External concepts -- $t5. Infinitesimals -- $t6. External analogues of internal notions -- $t7. Properties that hold almost everywhere -- $t8. L1 random variables 30 -- $t9. The decomposition of a stochastic process -- $t10. The total variation of a process -- $t11. Convergence of martingales -- $t12. Fluctuations of martingales -- $t13. Discontinuities of martingales -- $t14. The Lindeberg condition -- $t15. The maximum of a martingale -- $t16. The law of large numbers -- $t17. Nearly equivalent stochastic processes -- $t18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Lévy-Doob-Erdös-Kac-Donsker-Prokhorov theorem -- $tAppendix -- $tIndex
330   $aUsing only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
410  0$aAnnals of mathematics studies ;$vno. 117.
606   $aMartingales (Mathematics)
606   $aStochastic processes
606   $aProbabilities
610   $aAbraham Robinson.
610   $aAbsolute value.
610   $aAddition.
610   $aAlgebra of random variables.
610   $aAlmost surely.
610   $aAxiom.
610   $aAxiomatic system.
610   $aBorel set.
610   $aBounded function.
610   $aCantor's diagonal argument.
610   $aCardinality.
610   $aCartesian product.
610   $aCentral limit theorem.
610   $aChebyshev's inequality.
610   $aCompact space.
610   $aContradiction.
610   $aConvergence of random variables.
610   $aCorollary.
610   $aCorrelation coefficient.
610   $aCounterexample.
610   $aDimension (vector space).
610   $aDimension.
610   $aDivision by zero.
610   $aElementary function.
610   $aEstimation.
610   $aExistential quantification.
610   $aFamily of sets.
610   $aFinite set.
610   $aHyperplane.
610   $aIdealization.
610   $aIndependence (probability theory).
610   $aIndicator function.
610   $aInfinitesimal.
610   $aInternal set theory.
610   $aJoint probability distribution.
610   $aLaw of large numbers.
610   $aLinear function.
610   $aMartingale (probability theory).
610   $aMathematical induction.
610   $aMathematician.
610   $aMathematics.
610   $aMeasure (mathematics).
610   $aN0.
610   $aNatural number.
610   $aNon-standard analysis.
610   $aNorm (mathematics).
610   $aOrthogonal complement.
610   $aParameter.
610   $aPath space.
610   $aPredictable process.
610   $aProbability distribution.
610   $aProbability measure.
610   $aProbability space.
610   $aProbability theory.
610   $aProbability.
610   $aProduct topology.
610   $aProjection (linear algebra).
610   $aQuadratic variation.
610   $aRandom variable.
610   $aReal number.
610   $aRequirement.
610   $aScientific notation.
610   $aSequence.
610   $aSet (mathematics).
610   $aSignificant figures.
610   $aSpecial case.
610   $aStandard deviation.
610   $aStatistical mechanics.
610   $aStochastic process.
610   $aSubalgebra.
610   $aSubset.
610   $aSummation.
610   $aTheorem.
610   $aTheory.
610   $aTotal variation.
610   $aTransfer principle.
610   $aTransfinite number.
610   $aTrigonometric functions.
610   $aUpper and lower bounds.
610   $aVariable (mathematics).
610   $aVariance.
610   $aVector space.
610   $aW0.
610   $aWiener process.
610   $aWithout loss of generality.
615  0$aMartingales (Mathematics)
615  0$aStochastic processes.
615  0$aProbabilities.
676   $a519.2
700   $aNelson$b Edward, $0346945
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154754503321
996   $aRadically Elementary Probability Theory. (AM-117), Volume 117$92788042
997   $aUNINA