On transcendental directions of entire solutions of linear differential equations

This paper is devoted to studying the transcendental directions of entire solutions of f((n)) + A(n-1)f((n-1)) + ... + A(0)f = 0, where n(>= 2) is an integer and A(i)(z)(i = 0, 1, ..., n - 1) are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.