If [tex]x_n\geq 0, y_n\geq 0[/tex] and [tex]\lim \limits_{n \to \infty }x_n[/tex] exists, we have [tex]\limsup\limits_{n\to\infty}(x_n\cdot y_n)=(\lim\limits_{n\to\infty}x_n)\cdot(\limsup\limits_{n\to\infty}y_n)[/tex]. But if [tex]\lim\limits_{n\to\infty}x_n<0[/tex], do we have analog equation(I guess [tex]\limsup\limits_{n\to\infty}(x_n\cdot y_n)=(\lim\limits_{n\to\infty}x_n)\cdot(\liminf\limits_{n\to\infty }y_n)[/tex])? and what change should be made to conditions to achieve the analog equation? Formal source of reference such as textbooks or webpages is recommended. Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

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# A question about property of liminf and limsup

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