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Lebesgue Dominated Convergence example
How do I use Lebesgue Dominated Convergence Theorem to evaluate
$$\lim_{n \to \infty}\int_{[0,1]}\frac{n\sin(x)}{1+n^2\sqrt x}dx$$
What dominating function to use here?
- 3,407
34
votes
4
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Is there any difference between the notations $\int f(x)d\mu(x)$ and $\int f(x) \mu(dx)$?
Suppose $\mu$ is a measure. Is there any difference in meaning between the notation
$$\int f(x)d\mu(x)$$
and the notation
$$\int f(x) \mu(dx)$$?
- 519