Measure, Integral and Probability: Edition 2

ยท Springer Science & Business Media
แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜
311
แƒ’แƒ•แƒ”แƒ แƒ“แƒ˜
แƒ แƒ”แƒ˜แƒขแƒ˜แƒœแƒ’แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜ แƒ“แƒแƒฃแƒ“แƒแƒกแƒขแƒฃแƒ แƒ”แƒ‘แƒ”แƒšแƒ˜แƒ  แƒจแƒ”แƒ˜แƒขแƒงแƒ•แƒ”แƒ— แƒ›แƒ”แƒขแƒ˜

แƒแƒ› แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: ยท a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales ยท key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

แƒจแƒ”แƒแƒคแƒแƒกแƒ”แƒ— แƒ”แƒก แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜

แƒ’แƒ•แƒ˜แƒ—แƒฎแƒแƒ แƒ˜แƒ— แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒแƒ–แƒ แƒ˜.

แƒ˜แƒœแƒคแƒแƒ แƒ›แƒแƒชแƒ˜แƒ แƒฌแƒแƒ™แƒ˜แƒ—แƒฎแƒ•แƒแƒกแƒ—แƒแƒœ แƒ“แƒแƒ™แƒแƒ•แƒจแƒ˜แƒ แƒ”แƒ‘แƒ˜แƒ—

แƒกแƒ›แƒแƒ แƒขแƒคแƒแƒœแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒขแƒแƒ‘แƒšแƒ”แƒขแƒ”แƒ‘แƒ˜
แƒ“แƒแƒแƒ˜แƒœแƒกแƒขแƒแƒšแƒ˜แƒ แƒ”แƒ— Google Play Books แƒแƒžแƒ˜ Android แƒ“แƒ iPad/iPhone แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜แƒกแƒ—แƒ•แƒ˜แƒก. แƒ˜แƒก แƒแƒ•แƒขแƒแƒ›แƒแƒขแƒฃแƒ แƒแƒ“ แƒ’แƒแƒœแƒแƒฎแƒแƒ แƒชแƒ˜แƒ”แƒšแƒ”แƒ‘แƒก แƒกแƒ˜แƒœแƒฅแƒ แƒแƒœแƒ˜แƒ–แƒแƒชแƒ˜แƒแƒก แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒแƒœแƒ’แƒแƒ แƒ˜แƒจแƒ—แƒแƒœ แƒ“แƒ แƒกแƒแƒจแƒฃแƒแƒšแƒ”แƒ‘แƒแƒก แƒ›แƒแƒ’แƒชแƒ”แƒ›แƒ—, แƒฌแƒแƒ˜แƒ™แƒ˜แƒ—แƒฎแƒแƒ— แƒกแƒแƒกแƒฃแƒ แƒ•แƒ”แƒšแƒ˜ แƒ™แƒแƒœแƒขแƒ”แƒœแƒขแƒ˜ แƒœแƒ”แƒ‘แƒ˜แƒกแƒ›แƒ˜แƒ”แƒ  แƒแƒ“แƒ’แƒ˜แƒšแƒแƒก, แƒ แƒแƒ’แƒแƒ แƒช แƒแƒœแƒšแƒแƒ˜แƒœ, แƒ˜แƒกแƒ” แƒฎแƒแƒ–แƒ’แƒแƒ แƒ”แƒจแƒ” แƒ แƒ”แƒŸแƒ˜แƒ›แƒจแƒ˜.
แƒšแƒ”แƒžแƒขแƒแƒžแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ”แƒ‘แƒ˜
Google Play-แƒจแƒ˜ แƒจแƒ”แƒซแƒ”แƒœแƒ˜แƒšแƒ˜ แƒแƒฃแƒ“แƒ˜แƒแƒฌแƒ˜แƒ’แƒœแƒ”แƒ‘แƒ˜แƒก แƒ›แƒแƒกแƒ›แƒ”แƒœแƒ แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ˜แƒก แƒ•แƒ”แƒ‘-แƒ‘แƒ แƒแƒฃแƒ–แƒ”แƒ แƒ˜แƒก แƒ’แƒแƒ›แƒแƒงแƒ”แƒœแƒ”แƒ‘แƒ˜แƒ— แƒจแƒ”แƒ’แƒ˜แƒซแƒšแƒ˜แƒแƒ—.
แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒกแƒฎแƒ•แƒ แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜
แƒ”แƒšแƒ”แƒฅแƒขแƒ แƒแƒœแƒฃแƒšแƒ˜ แƒ›แƒ”แƒšแƒœแƒ˜แƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ–แƒ” แƒฌแƒแƒกแƒแƒ™แƒ˜แƒ—แƒฎแƒแƒ“, แƒ แƒแƒ’แƒแƒ แƒ˜แƒชแƒแƒ Kobo eReaders, แƒ—แƒฅแƒ•แƒ”แƒœ แƒฃแƒœแƒ“แƒ แƒฉแƒแƒ›แƒแƒขแƒ•แƒ˜แƒ แƒ—แƒแƒ— แƒคแƒแƒ˜แƒšแƒ˜ แƒ“แƒ แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒแƒ— แƒ˜แƒ’แƒ˜ แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒแƒจแƒ˜. แƒ“แƒแƒฎแƒ›แƒแƒ แƒ”แƒ‘แƒ˜แƒก แƒชแƒ”แƒœแƒขแƒ แƒ˜แƒก แƒ“แƒ”แƒขแƒแƒšแƒฃแƒ แƒ˜ แƒ˜แƒœแƒกแƒขแƒ แƒฃแƒฅแƒชแƒ˜แƒ”แƒ‘แƒ˜แƒก แƒ›แƒ˜แƒฎแƒ”แƒ“แƒ•แƒ˜แƒ— แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒ”แƒ— แƒคแƒแƒ˜แƒšแƒ”แƒ‘แƒ˜ แƒ›แƒฎแƒแƒ แƒ“แƒแƒญแƒ”แƒ แƒ˜แƒš แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ–แƒ”.