lebesgue integral - Finite measure space & sigma-finite measure space

A measure space $(X, \Sigma, \mu)$ is finite if $\mu(X)<\infty$.

It is equivalent to saying that $(X, \Sigma, \mu)$ is finite if $\mu(E)<\infty$ for all $E \in \Sigma$

A measure space $(X, \Sigma, \mu)$ is $\sigma$-finite if X is a countable union of sets with finite measure.

My two questions is that

1. Does $\sigma$-finiteness imply that $\mu(E)<\infty$ for all $E \in \Sigma$?




2. If $\mu(E)<\infty$ for all $E \in \Sigma$, dose it imply $\sigma$-finiteness or finiteness of a measure space?

Thanks.