UID:
edoccha_9958057477402883
Umfang:
1 online resource (399 pages)
ISBN:
1-281-74261-9
,
9786611742614
,
0-08-087325-1
Serie:
Pure and applied mathematics: a series of monographs and textbooks ; 13
Anmerkung:
Front Cover; Introduction to The Theory of Integration; Copyright Page; Contents; Preface; Chapter I. A General Theory of Limits; 1. Directed Sets . The Moore-Smith General Limit; 2. Properties of Limits; 3. Values Approached; 4. Extreme Limits; 5. Directed Sets of Sequential Character; 6. General Sums; 7. Double and Iterated Limits; 8. Filters; 9. Linear Spaces; Chapter II.Riemannian Type of Integration; 1. Functions of Intervals; 2. Integrals of Functions of Intervals; 3. Existence Theorems; 4. The Integral of an Interval Function as a Function of Intervals
,
5. Integral as a Function of the Interval Function; 6. Functions of Bounded Variation; 7. Continuity Properties of Functions of Bounded Vatiation; 8. The Space of Functions of Bounded Variation; 9. Riemann-Stieltjes integrals; 10. Existence Theorems for Riemann-Stieltjes Integrals; 11. Properties of Riemann-Stieltjes Integrals; 12. Classes of Functions Determined by Stieltjes Integrals; 13. Riemann-Stieltjes Integrals with Respect to Functions of Bounded Variation. Existence Theorems; 14. Properties of ?ab fdg with g of Bounded Variation on (a, b); 15. Convergence Theorems
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16. The Integral as a Function of the Upper Limit; 17. The Integral as a Function of a Parameter; 18. Linear Continuous Functionals on the Space of Continuous Functions; 19. Additional Definitions of Riemann Integrals of Stieltjes Type; 20. Stieltjes Integrals on Infinite Intervals; 21. A Linear Form on the Infinite Interval; Chapter III. Integrals of Riemann Type of Functions of Intervals In Two or Higher Dimension; 1. Interval Functions; 2. Subdivisions; 3. Integrals; 4. Functions of Bounded Variation in Two Dimensions; 5. Continuity Properties
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6. The Space of Functions of Bounded Variation in Two Variables: BV; 27. Functions of Bounded Variation According to Fréchet; 8. Riemann-Stieltjes Integrals in Two Variables; 9. Stieltjes Integrals in Two Dimensions with Respect to Functions of Bounded Variation; 10. Relation between Double and Iterated Integrals; 11. Double Integrals with Respect to Functions of Fréchet Bounded Variation; Chapter IV. Sets; 1. Fundamental Operations; 2. Characteristic Functions; 3. Properties of Classes of Sets; 4. Extensions of Classes of Sets Relative to Properties; Chapter V. Content and Measure
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1. Content of a Linear Bounded Set; 2. Properties of the Content Functions; 3. Borel Measurability; 4. General Lebesgue Measure of Linear Sets; 5. Lower Measure; 6. Measurability; 7. Examples of Measurable Sets; 8. Sets of Zero Measure; 9. Additional Properties of Upper and Lower Measure; 10. Additional Conditions for Measurability; 11. The Function a ( x ) I s Unbounded; 12. Lebesgue Measure; 13. Relation between a-Measure and Lebesgue Measure; 14. Relations between Classes of a-Measurable Sets; 15. Measurability of Sets in Euclidean Space of Higher Dimension; 16. Some Abstract Measure Theory; 17. Upper Semiadditive Functions
,
English
Weitere Ausg.:
ISBN 0-12-348050-7
Sprache:
Englisch
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