Скачать или смотреть |Lec-23|Defn of Integral of non-negative functions|Important theorems discussion

Measure and Integration Lecture-23
#Helpful In:- BSc./MSc./NET/GATE/NBHM/TIFR etc.
#topics discuss:-
#Definition of Integral of non-negative functions
#Theorem (1):-If f, g are non-negative measurable functions defined on E, then prove that
∫_E (f+g) = ∫_E f + ∫_E g
#Theorem (2):-If f and g are non-negative measurable functions defined on a measurable set E s.t. f is greater than g on E and f is integrable over E then g is also integrable on E
#Theorem (3):-Let f be a bounded measurable function defined on a measurable set E, such that f(x)≥0 and ∫_E f(x)dx = 0. Prove that f(x) = 0 a.e. in E, i.e., f(x) is equivalent to zero function on E

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