Taylor J.C. — An Introduction to Measure and Probability :: Электронная библиотека попечительского совета мехмата МГУ

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Taylor J.C. — An Introduction to Measure and Probability

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Название: An Introduction to Measure and Probability

Автор: Taylor J.C.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 324

Добавлена в каталог: 16.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Orthogonal system      154
Orthonormal system      154
Outer measure      21
Pairwise independent random variables      172
Parallelogram law      216
Parseval’s equality      155
Parseval’s relation      266
Parseval’s theorem      156
Partition $\pi$       49
Path      127
Poisson distribution      13
Poisson distribution with mean $\lambda>0$       38
Polish space      224
Predictable process      232
Principle of Mathematical Induction      7
Principle of monotone convergence      39
probability      6 9
Probability density function      56
Probability space      9
Product of a sequence of $\sigma$ -algebras      113
Product of complex numbers      289
Product of n probabilities      102
Product of n probability spaces      102
Product of two probabilities      99
Product of two probability spaces      99
Product topology      286
Projection operator      218
Pth absolute moment      140
Pth moment      140
Quantile transformation      259
Radon — Nikodym derivative of $\mathbf{P}$ with respect to $\lambda$       57
Radon — Nikodym theorem: measures      67
Radon — Nikodym theorem: signed measures      68
Random variable      32
Random variables      99
Random vector      86
Rational numbers      1
Real numbers      1
Regular Borel measure      151
Regular conditional probability      223
Riemann integrable      50
Riemann integral of $\varphi$ over [a,b]      50
Riesz representation theorem      217
Riesz — Fischer theorem      147
Right continuous      11
Right limit      11
Scheffe’s lemma      186
Second axiom of countability      87
Separable      224
Sequence of elements from      2
Set of Lebesgue measure zero      104
Signed measure      61
Simple function      30
Singular distribution function      see Cantor — Lebesgue function
Singular measure      57

Smooth      79 see
Square summable sequences      59
Standard deviation      140
Standard measurable spaces      224
Stochastic integral      232
Stochastic process      110
Stopping time      234
Strong Law of Large Numbers      170
Submartingale      229
Subsequence      2
Sufficient $\sigma$ -field      226
Sufficient statistic      227
Sup      see Supremum
Supermartingale      229
Supremum      20
Symmetric difference      78
Theorem of dominated convergence      43
Theorem of dominated convergence, equivalent form      44
Theorem of dominated convergence, first version      43
Three-series theorem      242
topology      14
Total variation      65 71
Trajectory      127
Transition kernel      120
Translation invariance      49
Translation invariant      49
Triangle inequality      5 146 216
Triangular array      280
Trigonometric polynomial      153
Truncation of a random variable at height c      180
Unbounded interval      4
Uniform closure      134
Uniform convergence      134
Uniform distribution on [0,1]      12
Uniform norm      153
Uniformly closed      134
Uniformly equicontinuous      283
Uniformly integrable      181
Uniqueness theorem, characteristic function      268
Unit normal distribution      13
Unit point mass at a      26
Unit point mass at the origin      26
Universally measurable sets      82
Upcrossing      245
Upper bound      1
Upper sum      49
Upper variation of $\nu$       62
Vanishing at infinity, Borel function      110
Variance      140
Vitali cover      195
Vitali Covering Lemma      195
Weak $L^1(\mathbb{R})$       187
Weak law of large numbers      170
Weak type      187
Weierstrass approximation theorem      175
Young’s inequality      142 201

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