Arithmetic Product Of Self-Similar Sets With Two Branches

For self-similar set E = lambda E-1 boolean OR (lambda E-2 + 1 - lambda(2)) (lambda(1) + lambda(2) < 1), we study the arithmetic product of E and obtain that when lambda(1) >= lambda(2) > 0 thenE . E = [0, 1]if and only if lambda(1) >= (1 - lambda(2))(2).To deal with the arithmetic product of self-similar sets with different ratios, we introduce a technique named comparable rectangle.