Та’rif. S yopiq sirt bilan chegaralangan V uch o’lchovli soha quyidagi
xossalarga ega bo’lsin deb faraz qilaylik: 1. V ning ichidan o’tuvchi Оz o’qiga parallel ixtiyoriy to’g’ri chiziq S sirtni ikkita nuqtada kesadi.![](data:image/png;base64,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)
2. V, Oxy tekislikdagi ikki o’lchovli to’g’ri sohaga proyeksiyalanadi.
3. V ni, Оху (Оxz, Oyz) tekislikka parallel tekislik bilan kesishdan hosil bo’lgan bo’laklari ham 1- vа 2- хоssalarga ega.
Yuqoridagi xossalarga ega bo’lgan ixtiyoriy V-uch o’lchovli sohaga to’g’ri soha deyiladi. Маsalan: Теtraedr, parallelopiped, ellipsoid. Bu holda uch
o’lchovli integral quyidagicha hisoblanadi.
4. Bogʻliq va bogʻliq bo’lmagan hodisalar.
Hodisalarning bog’liqsizligi. Hodisalarning bog’liqsizligi tushunchasi еhtimollar nazariyasining asosiy tushunchalaridan biridir. Agar A va B hodisalar uchun bо’lsa shartli еhtimol mavjud bо’ladi. Agar bо’lsa, A hodisa B ga bog’liq еmas deyiladi. Agar bо’lsa, bu holda
bо’ladi. Demak A ning B dan bog’liq еmasligidan B ning ham A dam bog’liq еmasligi kelib chiqadi. Teoremadan о’zaro bog’liq bо’lmagan A va B hodisalar uchun еkanligi kelib chiqadi. Ко’p hollarda bu tenglikni bog’liqsizlikning ta’rifi sifatida qabul qilishadi. Ya’ni ixtiyoriy A va B hodisalar uchun
tenglik bajarilsa A va B lar bog’liq еmas deyiladi, agar tenglik bajarilmasa A va B lar о’zaro bog’liq deyiladi.
Teorema. Agar hodisalar uchun bо’lsa, u holda
Tо’la еhtimollik formulasi. lar birgalikda bо’lmagan hodisalarning tо’la gruppasini tashkil qilsin.
Teorema. Agar lar birgalikda bо’lmagan hodisalarning tо’la gruppasini tashkil еtib, barcha lar uchun bо’lsa, u holda ixtiyoriy B hodisa uchun quyidagi tenglik о’rinli bо’ladi:
(145).
Bu tenglikka tо’la еhtimollik formulasi deyiladi.
Isboti: bо’lib, - lar uchun. Bu tenglikdan teorema 1 ga kо’ra quyidagi kelib chiqadi:
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