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  • Produktbild: An Introduction to Measure and Probability
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An Introduction to Measure and Probability

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

15.11.1996

Abbildungen

XVII, 324 p. 4 illus.

Verlag

Springer Us

Seitenzahl

324

Maße (L/B/H)

23,5/15,5/1,8 cm

Gewicht

487 g

Auflage

1997

Sprache

Englisch

ISBN

978-0-387-94830-0

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

15.11.1996

Abbildungen

XVII, 324 p. 4 illus.

Verlag

Springer Us

Seitenzahl

324

Maße (L/B/H)

23,5/15,5/1,8 cm

Gewicht

487 g

Auflage

1997

Sprache

Englisch

ISBN

978-0-387-94830-0

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: An Introduction to Measure and Probability
  • Produktbild: An Introduction to Measure and Probability
  • I. Probability Spaces.- 1. Introduction to ?.- 2. What is a probability space? Motivation.- 3. Definition of a probability space.- 4. Construction of a probability from a distribution function.- 5. Additional exercises*.- II. Integration.- 1. Integration on a probability space.- 2. Lebesgue measure on ? and Lebesgue integration.- 3. The Riemann integral and the Lebesgue integral.- 4. Probability density functions.- 5. Infinite series again.- 6. Differentiation under the integral sign.- 7. Signed measures and the Radon-Nikodym theorem*.- 8. Signed measures on ? and functions of bounded variation*.- 9. Additional exercises*.- III. Independence and Product Measures.- 1. Random vectors and Borel sets in ?n.- 2. Independence.- 3. Product measures.- 4. Infinite products.- 5. Some remarks on Markov chains*.- 6. Additional exercises*.- IV. Convergence of Random Variables and Measurable Functions.- 1. Norms for random variables and measurable functions.- 2. Continuous functions and Lp*.- 3. Pointwise convergence and convergence in measure or probability.- 4. Kolmogorov’s inequality and the strong law of large numbers.- 5. Uniform integrability and truncation*.- 6. Differentiation: the Hardy—Littlewood maximal function*.- 7. Additional exercises*.- V. Conditional Expectation and an Introduction to Martingales.- 1. Conditional expectation and Hilbert space.- 2. Conditional expectation.- 3. Sufficient statistics*.- 4. Martingales.- 5. An introduction to martingale convergence.- 6. The three-series theorem and the Doob decomposition.- 7. The martingale convergence theorem.- VI. An Introduction to Weak Convergence.- 1. Motivation: empirical distributions.- 2. Weak convergence of probabilities: equivalent formulations.- 3. Weak convergence of random variables.- 4.Empirical distributions again: the Glivenko—Cantelli theorem.- 5. The characteristic function.- 6. Uniqueness and inversion of the characteristic function.- 7. The central limit theorem.- 8. Additional exercises*.- 9. Appendix*.