sequences and series - What is meant by the absolute convergence of the infinite product $prodlimits_{n=1}^{infty} frac {1} {1+a_n}$?

Let $\{a_n \}$ be a sequence of real numbers. Consider the infinite product

$$\prod\limits_{n=1}^{\infty} \frac {1} {1+a_n}.$$

When do we say that the above infinite product is absolutely convergent? In the notion of an infinite series I know that a series $\sum\limits_{n=1}^{\infty} a_n$ is absolutely convergent if $\sum\limits_{n=1}^{\infty} |a_n|$ is convergent. For the case of infinite series I also know that absolute convergence implies convergence. Do all these results hold for infinite product too? Please help me in this regard.

Thank you so much for your valuable time.