اندازه و احتمال

توضیحات

این کتاب برای دانشجویان مقاطع کارشناسی ارشد و دکتری طراحی شده است. هدف کتاب پوشش میانی نظریه اندازه و نشریه احتمال است. ابتدا از طریق رویکرد اندازه خارجی کاراتیودوری، اندازه لبک ساخته و پس از آن انتگرال و قضایای حدی استاندارد مانند قضیه همگرایی یکنوا، قضیه همگرایی مغلو و همچنین لم‌فاتو بیان می‌شود. در ادامه عناصر نظریه احتمال از قبیل متغیرهای تصادفی، توزیع‌ها، استقلال، قضایای اندازه‌های حاصل‌ضرب، قانون اعداد بزرگ و قضیه حد مرکزی ارایه می‌شود. سپس زنجیرهای مارکوف زمان گسسته، توزیع های مانا و قضیه های حدید بحث و بررسی می‌شود. یک فصل کامل به اندازه‌های مختلط قضیه رادون- نیکودیم و قضیه نمایش ریش اختصاص یافته است. اثبات بدیل قضیه نمایش ریس و قانون اعداد بزرگ از ویژگی های برجسته کتاب است. سرانجام بسیاری از عنوان‌های اساسی همچون فضاهای متریک، فضاهای توپولوژیک و قضیه استون-0وایراشترلوس در ضمیمه کتاب مطرح ‌می‌شود.,

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اندازه و احتمال

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اس آر. آتریا - وی. اس. ساندر - دکتر رضا پورطاهری

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