We know that $\sum |f_n|$ converges on $E\subseteq \mathbb R$ then $\sum f_n$ is said to converge absolutely on $E$.
But in terms of pointwise or uniform convergence, I am willing to know what kind of convergence is the above. meaning by, if we say $\sum f_n$ is absolutely convergent, are we saying $\sum |f_n|$ is pointwise convergence or uniform convergence ?
Please clear my doubt. thanks in advance
Absolute convergence is pointwise convergence, because there is a statement which you mentioned, i.e. $\sum|f_n|$ -converges, then $\sum f_n$ - converges, and under convergence of $\sum f_n$ we mean poinwise covergence,if it was not mentioned previously about anything else. But it can also mean uniform convergence in special conditions (example is uniform convergence of $\sum\limits_{n=0}^{+\infty}c_n z^n$ on every compact subset of convergence circle )