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Lebl-Basic-Analysis-I
· Problem 6.2.3
Sequences of Functions
Mathematics · limit-of-integral
Problem
Let
f
:
[
0
,
1
]
→
R
f : [0,1] \to \mathbb{R}
f
:
[
0
,
1
]
→
R
be Riemann integrable (hence bounded). Find
lim
n
→
∞
∫
0
1
f
(
x
)
n
d
x
\displaystyle\lim_{n\to\infty} \int_0^1 \frac{f(x)}{n}\, dx
n
→
∞
lim
∫
0
1
n
f
(
x
)
d
x
.
Related theory
Limit Superior And Limit Inferior
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