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matan/sem2/KLK1/T/T17.typ
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*О связи модуля интеграла и интеграла от модуля*
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Пусть $f in R[a, b]$, тогда
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$
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- abs(integral_a^b d space d(x)) lt.eq abs(integral_a^b abs(f) space d(x))
+ abs(integral_a^b f space d(x)) lt.eq abs(integral_a^b abs(f) space d(x))
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*Док-во:*
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Интегрируемость функции $|f|$ известна из теоремы об арифмети-
matan/sem2/KLK1/test.pdf
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