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1.

図書
図書
1. Vector integration and stochastic integration in Banach spaces
Nicolae Dinculeanu
出版情報: New York : Wiley, c2000  xv, 424 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Preface
Vector Integration / Chapter 1：
Preliminaries / 1.：
Banach spaces / A.：
Classes of sets / B.：
Measurable functions / C.：
Simple measurability of operator-valued functions / D.：
Weak measurability / E.：
Integral of step functions / F.：
Totally measurable functions and the immediate integral / G.：
The Riesz representation theorem / H.：
The classical integral / I.：
The Bochner integral / J.：
Convergence theorems / K.：
Measures with finite variation / 2.：
The variation of vector measures
Boundedness of [sigma]-additive measures
Variation of real-valued measures
Integration with respect to vector measures with finite variation
The indefinite integral
Integration with respect to gm
The Radon-Nikodym theorem
Conditional expectations
[sigma]-additive measures / 3.：
[sigma]-additive measures on [sigma]-rings
Uniform [sigma]-additivity
Uniform absolute continuity and uniform [sigma]-additivity
Weak [sigma]-additivity
Uniform [sigma]-additivity of indefinite integrals
Weakly compact sets in L[superscript 1 subscript F] ([mu])
Measures with finite semivariation / 4.：
The semivariation
Semivariation and norming spaces
The semivariation of [sigma]-additive measures
The family m[subscript F,Z] of measures
Integration with respect to a measure with finite semivariation / 5.：
Measurability with respect to a vector measure
The seminorm m[subscript F,G](f)
The space of integrable functions
The integral
Properties of the space F[subscript D] (B, m[subscript F,G])
Relationship between the spaces F[subscript D](m)
The indefinite integral of measures with finite semivariation
Strong additivity / 6.：
Extension of measures / 7.：
Applications / 8.：
Integral representation of continuous linear operations on L[superscript p]-spaces
Random Gaussian measures
The Stochastic Integral / Chapter 2：
Summable processes / 9.：
Notations
The measure I[subscript X]
Computation of I[subscript X] for predictable rectangles
Computation of I[subscript X] for stochastic intervals
The stochastic integral / 10.：
The space F[subscript D] [characters not reproducible]
The integral [function of] HdI[subscript X]
A convergence theorem
The stochastic integral H - X
The stochastic integral and stopping times / 11.：
Stochastic integral of elementary processes
Stopping the stochastic integral
Summability of stopped processes
The jumps of the stochastic integral
The completeness of the space L[superscript 1 subscript F,G](X) / 12.：
The Uniform Convergence Theorem
The Vitali and the Lebesgue Convergence Theorems
The stochastic integral of [sigma]-elementary and of caglad processes as a pathwise Stieltjes integral
Summability of the stochastic integral / 13.：
Summability criterion / 14.：
Quasimartingales and the Doleans measure
The summability criterion
Local summability and local integrability / 15.：
Definitions
Basic properties
Additional properties
Martingales / Chapter 3：
Stochastic integral of martingales / 16.：
Square integrable martingales / 17.：
Extension of the measure I[subscript M]
Summability of square integrable martingales
Properties of the space F[subscript F,G](M)
Isometrical isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]])
Processes with Finite Variation / Chapter 4：
Functions with finite variation and their Stieltjes integral / 18.：
Functions with finite variation
The variation function |g|
The measure associated to a function
The Stieltjes integral
Processes with finite variation / 19.：
Definition and properties
Optional and predictable measures
The measure [mu subscript X]
Summability of processes with integrable variation
The stochastic integral as a Stieltjes integral
The pathwise stochastic integral
Semilocally summable processes
Processes with Finite Semivariation / Chapter 5：
Functions with finite semivariation and their Stieltjes integral / 20.：
Functions with finite semivariation
The Stieltjes integral with respect to a function with finite semivariation
Processes with finite semivariation / 21.：
The semivariation process
The measure [mu]x
Summability of processes with integrable semivariation
Dual projections / 22.：
Dual projection of measures
Dual projections of processes
Existence of dual projections
Processes with locally integrable variation or semivariation
Examples of processes with locally integrable variation or semivariation
Decomposition of local martingales
The Ito Formula / Chapter 6：
The Ito formula / 23.：
Preliminary results
The vector quadratic variation
The quadratic variation
The process of jumps
Ito's formula
Stochastic Integration in the Plane / Chapter 7：
Order relation in R[superscript 2] / 24.：
The increment [Delta subscript zz], g
Right continuity
The filtration
The predictable [Sigma]-algebra
Stopping times
Stochastic processes
Extension of processes from R[superscript 2 subscript +] [times] [Omega] to R[superscript 2] [times] [Omega]
The seminorm I[subscript X] and the space F[subscript F,G](X) / 25.：
Properties of the stochastic integral / 26.：
Extension of I[subscript X] to P([infinity])
Existence of left limits of X in L[superscript p subscript E]
Some properties of the integral [function of] HdI[subscript X]
Two-Parameter Martingales / Chapter 8：
A decomposition theorem / 27.：
The measures [characters not reproducible] and [mu subscript [M]]
Summability of the square integrable martingales in Hilbert spaces
The space F[subscript F,G](I[subscript M])
Isometric isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]])
Two-Parameter Processes with Finite Variation / Chapter 9：
Functions with finite variation in the plane / 29.：
Monotone functions
Partitions
Variation corresponding to a partition
Variation of a function on a rectangle
Limits of the variation
Functions vanishing outside a quadrant
Variation of real-valued functions
Lateral limits
Measures associated to functions
[sigma]-additivity of the measure m[subscript g] / L.：
Processes with integrable variation / M.：
Two-Parameter Processes with Finite Semivariation / Chapter 10：
Functions with finite semivariation in the plane / 31.：
The Stieltjes integral for functions with finite semivariation in R[superscript 2]
Processes with finite semivariation in the plane / 32.：
References
Preface
Vector Integration / Chapter 1：
Preliminaries / 1.：
2.

図書
図書
2. Lectures on real and complex vector spaces
[by] Frank S. Cater
出版情報: Philadelphia : Saunders, 1966  x, 167 p. ; 24 cm
シリーズ名: Saunders mathematics books
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3.

図書
図書
3. Calculus in vector spaces
Lawrence J. Corwin, Robert H. Szczarba
出版情報: New York : M. Dekker, c1979  x, 782 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 52
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4.

図書
図書
4. Finite and infinite dimensional linear spaces : a comparative study in algebraic and analytic settings
Richard D. Järvinen
出版情報: New York : M. Dekker, c1981  xiv, 168 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 66
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5.

図書
図書
5. Linear spaces with few lines (: gw ; : us)
Klaus Metsch
出版情報: Berlin : Tokyo : Springer-Verlag, c1991  xi, 195 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1490
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6.

図書
図書
6. Vector spaces and matrices
Robert M. Thrall and Leonard Tornheim
出版情報: New York : J. Wiley, [1957]  318 p. ; 24 cm
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7.

図書
図書
7. Module theory : an approach to linear algebra. 2nd ed (pbk.)
T.S. Blyth
出版情報: Oxford [England] : Clarendon Press , New York : Oxford University Press, 1990  vi, 360 p. ; 24 cm
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目次情報: 続きを見る
Modules, Vector Spaces and Algebras / 1：
Submodules; Intersections and Sums / 2：
Morphisms; Exact Sequences / 3：
Quotient Modules; Basic Isomorphism Theorems / 4：
Chain Conditions; Jordan-Holder Towers / 5：
Products and Coproducts / 6：
Free Modules; Bases / 7：
Groups of Morphisms; Projective Modules / 8：
Duality; Transposition / 9：
Matrices; Linear Equations / 10：
Inner Product Spaces / 11：
Injective Modules / 12：
Simple and Semisimple Modules / 13：
The Jacobson Radical / 14：
Tensor Products; Flat Modules; Regular Rings / 15：
Tensor Products; Tensor Algebras / 16：
Exterior Algebras, Determinants / 17：
Modules Over A Principal Ideal Domain; Finitely Generated Abelian Groups / 18：
Vector Space Decomposition Theorems; Canonical Forms Under Similarity / 19：
Diagonalisation; Normal Transformations / 20：
Modules, Vector Spaces and Algebras / 1：
Submodules; Intersections and Sums / 2：
Morphisms; Exact Sequences / 3：
8.

図書
図書
8. Elements of continuous multivariate analysis
[by] A. P. Dempster
出版情報: Reading, Mass. : Addison-Wesley Pub. Co, c1969  xii, 388 p ; 23 cm
シリーズ名: Addison-Wesley series in behavioral science : quantitative methods
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9.

図書
図書
9. Lectures on groups and vector spaces for physicists (: pbk)
Chris J. Isham
出版情報: Singapore : World Scientific, c1989  vii, 219 p. ; 23 cm
シリーズ名: World Scientific lecture notes in physics ; v. 31
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10.

図書
図書
10. Metric planes and metric vector spaces
Rolf Lingenberg
出版情報: New York : Wiley, c1979  xi, 209 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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