By Lemma 2.4 and max{[sigma]([f.sup.(k)]), [sigma]([A.sub.j][f.sup.(j)]), [sigma]([B.sub.j][f.sup.(j)]) (j = 0,1, ..., k - 1)} < n, for any given [epsilon](0 < 2[epsilon] < 1), there exists a set [E.sub.5] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have

By Lemma 2.1, there exist a constant B > 0 and a set [E.sub.1] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z satisfying [absolute value of z] = r [not member of] [0,1] [union] [E.sub.1], we have

By Lemma 2.2, there exist a sequence [{[r.sub.m]}.sub.m[member of]N], [r.sub.m] [right arrow] +[infinity] and a set [E.sub.2] of finite logarithmic measure such that the estimation

By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min{1,n - [beta]}), there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have

By Lemma 2.4, for any given [epsilon](0 < 2[epsilon] < min {1, n - [beta]}), there exists a set [E.sub.5] [subset] (1, +[infinity] having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have

By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min {1 - c/1 + c, n - [beta]}), there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have

By Lemma 2.4, for any given [epsilon](0 < 2[epsilon] < min{1 - c/1 + c, n - [beta]}), there exists a set [E.sub.5] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have (3.31) and

By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min {1, n - [beta]}) there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have (3.29) and (3.30).