1. The set $A=\left\{n \left\lvert\, \lg n<\frac{1}{2}\right., n \in \mathbf{N}^{*}\right\}$ has the sum of all its elements as $\qquad$
$\lg n<\frac{1}{2} \Rightarrow 0<n<\sqrt{10} \Rightarrow n=1,2,3$, so the sum of all elements in set $A$ is 6.