000			03534cam a2200433Ki 4500
001			ocn876589188
003			OCoLC
005			20190328114807.0
006			m o d
007			cr cnu---unuuu
008			140414s2014 ne ob 001 0 eng d
040			_aOPELS _beng _erda _epn _cOPELS _dYDXCP _dUKMGB _dTEFOD _dOCLCF _dOCLCQ _dTEFOD _dOCLCQ _dU3W _dD6H _dOTZ _dYDX _dWYU
016	7		_a016709723 _2Uk
020			_a9780128002902 _q(electronic bk.)
020			_a0128002905 _q(electronic bk.)
020			_z9780128000427
035			_a(OCoLC)876589188
050		4	_aQA273 _b.R864 2014eb
082	0	4	_a519.2 _223
100	1		_aRoussas, George G., _eauthor.
245	1	3	_aAn introduction to measure-theoretic probability / _h[electronic resource] _cby George G. Roussas.
250			_a2nd ed.
264		1	_aAmsterdam ; _aNew York : _bAcademic Press, an imprint of Elsevier, _c2014.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
520			_a"In this introductory chapter, the concepts of a field and of a [sigma]-field are introduced, they are illustrated bymeans of examples, and some relevant basic results are derived. Also, the concept of a monotone class is defined and its relationship to certain fields and [sigma]-fields is investigated. Given a collection of measurable spaces, their product space is defined, and some basic properties are established. The concept of a measurable mapping is introduced, and its relation to certain [sigma]-fields is studied. Finally, it is shown that any random variable is the pointwise limit of a sequence of simple random variables"-- _cProvided by publisher.
504			_aIncludes bibliographical references and index.
588	0		_aPrint version record.
505	0		_aCertain classes of sets, measurability, and pointwise approximation -- Definition and construction of a measure and its basic properties -- Some modes of convergence of sequences of random variables and their relationships -- The integral of a random variable and its basic properties -- Standard convergence theorems, the Fubini theorem -- Standard moment and probability inequalities, convergence in the rth mean and its implications -- The Hahn-Jordan decomposition theorem, the Lebesgue decomposition theorem, and the Radon-Nikodym theorem -- Distribution functions and their basic properties, Helly-Bray type results -- Conditional expectation and conditional probability, and related properties and results -- Independence -- Topics from the theory of characteristic functions -- The central limit problem: the centered case -- The central limit problem: the noncentered case -- Topics from sequences of independent random variables -- Topics from Ergodic theory -- Two cases of statistical inference: estimation of a real-valued parameter, nonparametric estimation of a probability density function -- Appendixes: A. Brief review of chapters 1-16 -- B. Brief review of Riemann-Stieltjes integral -- C. Notation and abbreviations.
650		0	_aProbabilities.
650		0	_aMeasure theory.
650		7	_aMeasure theory. _2fast _0(OCoLC)fst01013175
650		7	_aProbabilities. _2fast _0(OCoLC)fst01077737
655		4	_aElectronic books.
776	0	8	_iPrint version: _aRoussas, George G. _tIntroduction to measure-theoretic probability. _bSecond edition _z9780128000427 _w(DLC) 2014007243 _w(OCoLC)868642456
856	4	0	_3ScienceDirect _uhttp://www.sciencedirect.com/science/book/9780128000427
999			_c246899 _d246899