Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Saks S. — Theory of the integral, Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Theory of the integral, Автор: Saks S. Аннотация: Covering all the standard topics, the author begins with a discussion of the integral in an abstract space, additive classes of sets, measurable functions, and  integration of sequences of functions. Succeeding chapters cover Carath?odory measure; functions of bounded variation and the Lebesgue-Stieltjes integral; the derivation of additive functions of a set and of an interval; more. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-d edition Год издания: 1937 Количество страниц: 354 Добавлена в каталог: 25.11.2012 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель
 Almost      16 angle      310 Area, Elementary, of a polyhedron      165 Area, of a continuous surface      165 Area, of an interval      59 Boundary of a set      40 Centre, of a dosed sphere      40 Centre, of an open sphere      40 Chain of points      122 Classes of sets, Additive      7 Classes of sets, Additive in the weak sense      7 Classes of sets, Complete with respect to a measure      86 Classes of sets, Completely additive      7 Closure of a set      40 Coefficients of an approximate differential      300 Complement of a set      6 Condition, ( )      192 Condition, ( )      192 Condition, ( )      192 Condition, ( )      277 Condition, ( )      277 Condition, (D)      290 Condition, (S)      282 Condition, Luain's, (N)      224 Condition, of Lipschitz for functions of a real variable on a Bet      264 Condition, of Lipschitz for functions of two variables on a set      304 Condition, of Lipschitz for functions of two variables on an interval      169 Contingent      263 Coordinates of a point      56 Covering in the sense of Vitali      109 Cubes      57 Cubes, Half open      57 Cubes, Open      57 CURVES      121 Curves, rectifiable      122 Curves, rectifiable on an interval      122 Decomposition, Jordan, of a function of a set      11 Decomposition, Jordan, of a function of an interval      62 Decomposition, Lebesgue, of a function of a set      35 Decomposition, Lebesgue, of a function of an interval      120 Densities, Outer upper and lower      128 Densities, Right-hand and left-hand      215 Densities, Upper and lower      129 Derivates, (Ordinary) upper and lower      106 Derivates, Approximate bilateral, upper and lower      220 Derivates, Approximate right-hand and left-hand, upper and lower      220 Derivates, Bilateral      108 Derivates, Dini      108 Derivates, Extreme      106 Derivates, General upper and lower      100 Derivates, Intermediate      108 Derivates, Opposite      269 Derivates, relative to a set      108 Derivates, Strong upper and lower      106 Derivates, Symmetrical, upper and lower      149 Derivates, Unilateral (right- and left-hand)      108 Derivates, Unique      106 Derivates, with respect to a function      108 Derivates, with respect to a measure and a sequence of nets in a metrical apace      154 Derivates, with respect to a sequence of nets of intervals      188 Derivative, approximate      220 Derivative, General      106 Derivative, of a complex function      196 Derivative, ordinary      106 Derivative, relative to a set      108 Derivative, Roussel      210 Derivative, strong      106 Derivative, Unilateral      108 Derivative, with respect to a function      109 Derivative, with respect to a measure and a sequence of nets in a metrical space      154 Derivative, with respect to a sequence of nets of intervals      188 Diameter      40 Difference of sets      5 Differential, Approximate      300 Differential, Extreme      309 Differential, total      300 Differential, Upper and lower      309 Direction of a half-line      262 Distance, of a point and a set      40 Distance, of points      39 Distance, of points in an Euclidean space      56 Distance, of points in the torus space      157 Distance, of sets      40 Element of a set      4 Expressions of de Geocze      171 Faces of a polyhedron      164 Faces of an interval      57 Families of sets      see "Clashes of sets" figure      58 Figure, Elementary      58 Function (of a point)      see also "Functions (of an interval)" "Functions Function (of a point), Approximately continuous      132 Function (of a point), Characteristic, of sets      6 Function (of a point), Continuous      42 Function (of a point), Cylindrical      159 Function (of a point), Equimeasurable      143 Function (of a point), Finite      6 Function (of a point), Integrable      20 Function (of a point), integrable in the Lebesgue sense      65 Function (of a point), integrable in the Lebesgue — Stieltjes sense      65 Function (of a point), Measurable      12 Function (of a point), Simple      7 Function (of a point), Summable      65 Function (of a point), Upper and lower semi-continuous      42 Function of singularities, of a function of a set      35 Function of singularities, of a function of an interval      120 Functions (of a complex variable), Complex      195 Functions (of a complex variable), Derivable      196 Functions (of a complex variable), Holomorphic      195 Functions (of a real variable)      96 see "Functions Functions (of a real variable), 231 Functions (of a real variable), 231 Functions (of a real variable), 228 Functions (of a real variable), 228 Functions (of a real variable), -integrable      241 Functions (of a real variable), -integrable      241 Functions (of a real variable), -integrable      201 Functions (of a real variable), Absolutely continuous      96 Functions (of a real variable), absolutely continuous (in the wide sense)      223 Functions (of a real variable), absolutely continuous in the restricted sense      231 Functions (of a real variable), AC      223 Functions (of a real variable), ACG      223 Functions (of a real variable), Approximately derivable      220 Functions (of a real variable), continuous in the sense of Darboux      272 Functions (of a real variable), generalized absolutely continuous (in the wide sense)      223 Functions (of a real variable), generalized absolutely continuous in the restricted sense      231 Functions (of a real variable), Inner and outer, of a superposition      286 Functions (of a real variable), integrable in the sense of Newton      156 Functions (of a real variable), integrable in the sense of Perron      201 Functions (of a real variable), Inverse      286 Functions (of a real variable), of bounded variation      96 Functions (of a real variable), of bounded variation (in the wide sense)      221 Functions (of a real variable), of generalized bounded variation (in the wide sense)      221 Functions (of a real variable), of generalized bounded variation in the restricted sense      228 Functions (of a real variable), of hounded variation in the restricted sense      228 Functions (of a real variable), Regular      97 Functions (of a real variable), Saltus      97 Functions (of a real variable), Singular      96 Functions (of a real variable), VB      221 Functions (of a real variable), VBG      221 Functions (of a set), Absolutely continuous      30 66 Functions (of a set), Additive      8 Functions (of a set), Monotone      8 Functions (of a set), Non-decreasing and non-increasing      5 Functions (of a set), Singular      30 66 Functions (of an interval)      59 see Functions (of an interval) of bounded variation      61 Functions (of an interval), Absolutely continuous      93 Functions (of an interval), Additive      61 Functions (of an interval), Continuous      59 Functions (of an interval), continuous and discontinuous at a hyperplane      60 Functions (of an interval), Major and minor      191 Functions (of an interval), Major and minor, with respect to a function      207 Functions (of an interval), Monotone non-decreasing and non -increasing      61 Functions (of an interval), Singular      93 Functions (of two real variables), Absolutely continuous      169 Functions (of two real variables), Approximately different]able      300 Functions (of two real variables), Differentiable      300 Functions (of two real variables), of bounded variation      169 Functions (of two real variables), Totally differentiate      300 Graph, of a curve      121 Graph, of a function      88 Half-plane      263 264 Half-space      263 306 Half-tangent, Intermediate      262 Hyperplane      57 Hyperplane, Extreme tangent      263 Hyperplane, Intermediate tangent      263 Hyperplane, orthogonal to an axis      57 Hyperplane, tangent      263 Hyperplane, Unique tangent      263 Increment of a function      96 Integrals      241 Integrals, -      241 Integrals, -      241 Integrals, -      207 Integrals, -      201 Integrals, -      244 Integrals, Compatible      254 Integrals, definite      19 20 46 254 Integrals, Definite and indefinite Burkill      166 Integrals, Denjoy — Khintchine      241 Integrals, Denjoy — Perron      241 Integrals, Denjoy, in the restricted sense      241 Integrals, Denjoy, in the wide House      241 Integrals, indefinite      29 254 Integrals, Lebesgue      65 Integrals, Lebesgue — Stieltjes      65 Integrals, Mean value      178 Integrals, Perron      201 Integrals, Perron — Stieltjes      207 Integrals, Upper and lower Burkill      166 Interior of a set      40 Intervals      57 Intervals, closed      57 Intervals, Degenerate      57 Intervals, Half-open      57 Intervals, in the torus space      157 Intervals, open      57 Length of a curve      122 Length of a set      54 Length of an interval      59 Length of arc of a curve      122 Length, Outer, of a set      54 Limit, approximate      219 Limit, Approximate bilateral and unilateral      220 Limit, Approximate extreme      219 Limit, Approximate, upper and lower      218 Limit, of a sequence of points      39 Limit, of a sequence of seta      5 Limit, Upper and lower, of a sequence of Bets      5 Lines, straight      56 57 Maximum, of a function at a point      42 Maximum, Strict      261 Measure      16 Measure, function      117 Measure, in the torus space      158 Measure, Lebesgue      65 Measure, of a Bet      46 Measure, Outer Caratheodory      43 Measure, Outer Lebesgue      65 Measure, Outer linear, of a, set on a line      297 Measure, Outer, in the torus space      157 Measure, Outer, of a set      46 Measure, Regular outer      50 Mesh of a net      153 Minimum, of a function at a point      42 Minimum, strict      261 Neighbourhood of a point      40 Net, in a metrical spate      153 Net, Normal, of intervals      188 Net, of closed intervals      57 Net, of half open intervals      57 Nucleus of a determining system      47 Number, Characteristic, of a family of sets      40 Operation (A)      47 Ordinate-set of a function      88 Oscillation, of a function of a point at a point      42 Oscillation, of a function of an interval at a set      60 Oscillation, of a function of an interval on a set      60 Parameter, of a curve      121 Parameter, of regularity of a set      106 Part, Absolutely continuous, of a function of an interval      120 Part, Common, of sets      5 Part, Non-negative and non-positive, of a function      13 Part, Real and imaginary, of a complex function      195 Plane      56 57 see Plane, Whole      264 Points, internal      40 Points, isolated      40 Points, isolated on the right or the left      215 Points, of a curve      121 Points, of a space      6 Points, of accumulation      40 Points, of density      129 Points, of dispersion      128 Points, of linear density in the direction nf an axis      298 Points, of outer density      128 Points, Right- and left-hand, of accumulation      215 Points, Unilateral (right- and left-hand), of outer density      215 Polyhedron      164 Portion of a set      41 Primitive of Newton      186 Product of sets      5 Product of sets, Cartesian      82 Product of sets, Combinatory      82 Radius, of a closed sphere      40 Radius, of a neighbourhood      40 Radius, of an open sphere      40 Relations, Denjoy      269 Sequences, Ascending and descending, of sets      5 Sequences, Binary, of nets of intervals      191 Sequences, Convergent, of points      40 Sequences, Convergent, of sets      5 Sequences, Monotone, of sets      5 Sequences, Non-decreasing and non-increasing, of sets      5 Sequences, Normal, of nets of intervals      188 Sequences, of mean value integrals      178 Sequences, Regular, of nets in a metrical space      153 Sequences, Regular, of nets of intervals      57 Sets, ( )      41 Sets, ( )      40 Sets, ( )      40 Sets, Borel      41 Sets, bounded      40 Sets, closed      40 Sets, Cylindrical, in the torus space      159 Sets, Derived      40 Sets, dosed in a set      41 Sets, empty      4 Sets, Enumerable      4 Sets, everywhere dense in a set      41 Sets, Isolated      40 Sets, Linear      56 Sets, measurable      7 Sets, measurable ( )      41 Sets, measurable with respect to an outer Caratheodory measure      44 Sets, Measurable, in the torus space      159 Sets, non-dense in a set      41 Sets, Non-overlapping      40
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