Beyes formulalari.
Teorema. lar birgalikda bо’lmagan hodisalarning tо’la gruppasi bо’lsin va . Agar ixtiyoriy B - hodisa uchun bо’lsa, u holda quyidagi tenglik о’rinli bо’ladi.
5. Birinchi va ikkinchi tur egri chiziqli integrallarning ta’rifi, ularning xossalari va ularni hisoblash.
Ushbu ![](data:image/png;base64,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) funksiyalar kesmada aniqlangan va uzluksiz bo`lib, ular ning turli qiymatlariga da turli nuqtalarni mos qo`ysin. Bu holda kesmaning
funksiyalar yordamida da hosil bo`ladigan aksi ga sodda egri chiziq deyiladi: .
ga egri chiziqning boshlang`ich nuqtasi nuqtaga esa egri chiziqning oxirgi nuqtasi deb ataladi. Biz qaralayotgan egri chiziq to`g`rilanuvchi, ya`ni chekli uzunlikka ega bo`lsin deb faraz qilamiz.
Aytaylik, xOy tekisligida biror sodda egri chiziq yoyi va bu yoyda funksiya berilgan bo`lsin. egri chiziqni A dan V ga qarab nuqtalar yordamida n ta ( ) yoyga ajratamiz. yoyning uzunligini va deb belgilaymiz. Endi nuqtalar olamiz va quyidagi
yig`indini tuzamiz. Ta`rif. Agar bo`lib, u chekli I soniga teng bo`lsa va I ning qiymati ning bo`linish usuliga hamda nuqtalarning tanlanishiga bog`liq bo`lmasa, u holda shu I soniga funksiyaning egri chiziq bo`yicha birinshi tur egri chiziqli integralideb ataladi va u kabi belgilanadi. Shunday qilib,
![](data:image/png;base64,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) ekan.
Birinchi tur egri chiziqli integrallar quyidagi xossalarga ega.
Do'stlaringiz bilan baham: |