Stieltjes Integral
-10%
portes grátis
Stieltjes Integral
Convertito, Gregory; Cruz-Uribe, David
Taylor & Francis Inc
02/2023
250
Dura
Inglês
9780815374008
15 a 20 dias
Descrição não disponível.
1. The Darboux Integral. 1.1. Bounded, Continuous, and Monotonic Functions. 1.2. Step Functions. 1.3. The Darboux Integral. 1.4. Properties of the Darboux Integral. 1.5. Limits and the Integral. 1.6. The Fundamental Theorem of Calculus. 1.7. Exercises. 2. Further Properties of the Integral. 2.1. The Lebesgue Criterion. 2.2. The Riemann Integral. 2.3. Integrable Functions as a Normed Vector Space. 2.4. Exercises. 3. Functions of Bounded Variation. 3.1. Monotonic Functions. 3.2. Functions of Bounded Variation. 3.3. Properties of Functions of Bounded Variation. 3.4. Limits and Bounded Variation. 3.5. Discontinuities and the Saltus Decomposition. 3.6. BV [a; b] as a Normed Vector Space. 3.7. Exercises. 4. The Stieltjes Integral. 4.1. The Stieltjes Integral of Step Functions. 4.2. The Stieltjes Integral with Increasing Integrator. 4.3. The Stieltjes Integral with BV Integrator. 4.4. Existence of the Stieltjes Integral. 4.5. Limits and the Stieltjes Integral. 4.6. Exercises. 5. Further Properties of the Stieltjes Integral. 5.1. The Stieltjes Integral and Integration by Parts. 5.2. The Lebesgue-Stieltjes Criterion. 5.3. The Riemann-Stieltjes Integral. 5.4. The Riesz Representation Theorem. 5.5. Exercises.
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Darboux Integral;Bounded Variation;Lebesgue Criterion;Riesz representation;Integrability theorems
1. The Darboux Integral. 1.1. Bounded, Continuous, and Monotonic Functions. 1.2. Step Functions. 1.3. The Darboux Integral. 1.4. Properties of the Darboux Integral. 1.5. Limits and the Integral. 1.6. The Fundamental Theorem of Calculus. 1.7. Exercises. 2. Further Properties of the Integral. 2.1. The Lebesgue Criterion. 2.2. The Riemann Integral. 2.3. Integrable Functions as a Normed Vector Space. 2.4. Exercises. 3. Functions of Bounded Variation. 3.1. Monotonic Functions. 3.2. Functions of Bounded Variation. 3.3. Properties of Functions of Bounded Variation. 3.4. Limits and Bounded Variation. 3.5. Discontinuities and the Saltus Decomposition. 3.6. BV [a; b] as a Normed Vector Space. 3.7. Exercises. 4. The Stieltjes Integral. 4.1. The Stieltjes Integral of Step Functions. 4.2. The Stieltjes Integral with Increasing Integrator. 4.3. The Stieltjes Integral with BV Integrator. 4.4. Existence of the Stieltjes Integral. 4.5. Limits and the Stieltjes Integral. 4.6. Exercises. 5. Further Properties of the Stieltjes Integral. 5.1. The Stieltjes Integral and Integration by Parts. 5.2. The Lebesgue-Stieltjes Criterion. 5.3. The Riemann-Stieltjes Integral. 5.4. The Riesz Representation Theorem. 5.5. Exercises.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
