**Definition:** Suppose $\mathcal A$ is
the Boolean algebra of all Jordan measurable sets in $I=[0,1]$ (i.e $\mathcal A=\{A\subseteq I: \mu(\partial(A))=0\}$, where $\mu$ is the Lebesgue measure and $\partial$ means the topological boundary).

**Definition:** "Interval algebra" suppose $\mathcal B$ on $I=[0,1]$ is the algebra generated by the sets of the form $([a_{0},b_{0})\cup[a_{1},b_{1})\cup...\cup[a_{n},b_{n}))\cap I$ where $0\leq a_{0}< b_{0}<a_{1}<b_{1}<...<a_{n}<b_{n}$.

(1) Prove or disprove: Every (nontrivial) uncountable atomless subalgebra of $\mathcal A$ is isomorphic to $\mathcal B$.

(2) If (1) is false, I would say: Every (nontrivial) uncountable atomless subalgebra of $\mathcal A/N$ ($N$ is the family of all null sets) is isomorphic to $\mathcal B$.

By atomless I mean a Boolean algebra which has no atom.