ERDŐS PROPERTIES OF SUBSETS OF THE MAHLER SET <i>S</i>

Abstract Erdős proved that every real number is the sum of two Liouville numbers. A set W complex numbers said to have property if members . Mahler divided all transcendental into three disjoint classes S , T and U such that, in particular, any which are algebraically dependent lie same class. The a proper subset has Lebesgue measure zero. It here, using theorem Weil on locally compact groups, $m\in [0,\infty )$ then there exist $2^{\mathfrak {c}}$ dense subsets each m no these homeomorphic. also full measure, property. Finally, it