Non-Additive Measure and Integral
D. Denneberg
03.2013β―Π³. Β· Theory and Decision Library B ΠΠ½ΠΈΠ³Π° 27 Β· Springer Science & Business Media
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
178
Π‘ΡΡΠ°Π½ΠΈΡΠΈ
reportΠΡΠ΅Π½ΠΊΠΈΡΠ΅ ΠΈ ΠΎΡΠ·ΠΈΠ²ΠΈΡΠ΅ Π½Π΅ ΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΄Π΅Π½ΠΈ Β ΠΠ°ΡΡΠ΅ΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΡΠΈΡΠΊΠΎ Π·Π° ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc.
Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory.
In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.
Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory.
In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.
ΠΡΠ΅Π½Π΅ΡΠ΅ ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
ΠΠ°ΠΆΠ΅ΡΠ΅ Π½ΠΈ ΠΊΠ°ΠΊΠ²ΠΎ ΠΌΠΈΡΠ»ΠΈΡΠ΅.
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Π‘ΠΌΠ°ΡΡΡΠΎΠ½ΠΈ ΠΈ ΡΠ°Π±Π»Π΅ΡΠΈ
ΠΠ½ΡΡΠ°Π»ΠΈΡΠ°ΠΉΡΠ΅ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΡΠΎ Google Play ΠΠ½ΠΈΠ³ΠΈ Π·Π° Android ΠΈ iPad/iPhone. Π’ΠΎ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ½ΠΎ ΡΠ΅ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΠΈΡΠ° Ρ ΠΏΡΠΎΡΠΈΠ»Π° Π²ΠΈ ΠΈ Π²ΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ²Π° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈΠ»ΠΈ ΠΎΡΠ»Π°ΠΉΠ½, ΠΊΡΠ΄Π΅ΡΠΎ ΠΈ Π΄Π° ΡΡΠ΅.
ΠΠ°ΠΏΡΠΎΠΏΠΈ ΠΈ ΠΊΠΎΠΌΠΏΡΡΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π·Π°ΠΊΡΠΏΠ΅Π½ΠΈΡΠ΅ ΠΎΡ Google Play Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ ΡΠ΅Π± Π±ΡΠ°ΡΠ·ΡΡΠ° Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΡΠ° ΡΠΈ.
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΡΡΠΎΠΉΡΡΠ²Π°
ΠΠ° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²Π° Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎ ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΡΠΎ Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈΡΠ΅ ΡΠ΅ΡΡΠΈ ΠΎΡ Kobo, ΡΡΡΠ±Π²Π° Π΄Π° ΠΈΠ·ΡΠ΅Π³Π»ΠΈΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎΡΠΎ ΡΠΈ. ΠΠ·ΠΏΡΠ»Π½Π΅ΡΠ΅ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΈΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π² ΠΠΎΠΌΠΎΡΠ½ΠΈΡ ΡΠ΅Π½ΡΡΡ, Π·Π° Π΄Π° ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ ΡΠ°ΠΉΠ»ΠΎΠ²Π΅ΡΠ΅ Π² ΠΏΠΎΠ΄Π΄ΡΡΠΆΠ°Π½ΠΈΡΠ΅ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ.
