I have a integral with the following property: $$ \forall n>0,\quad \int_X f_n(x) dx> 0 $$ I am trying to be able to say that: $$ \int_X \hspace{.5em}\lim_{n\rightarrow 0} \hspace{.5em}f_n(x)dx > 0 $$ Is it adequate to say: $$\text{Since, }\forall n \in \mathbb{N}, \frac{1}{n}>0 \Rightarrow \int_X f_{\frac{1}{n}}(x)dx > 0 \Rightarrow \int_X \hspace{.5em}\lim_{n\rightarrow \infty} \hspace{.5em}f_{\frac{1}{n}}(x) dx> 0$$ Or is this incorrect?
2026-02-23 06:37:59.1771828679
Understanding the integral of a sequence of functions
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