Abstract: | We consider the set of regular functions
H = { f:f = z + ?n = 2¥ nbn zn ,|bn | \leqslant 1} on |z| < 1H = \{ f:f = z + \sum\limits_{n = 2}^\infty {nb_n z^n ,|b_n |{\mathbf{ }} \leqslant 1\} {\mathbf{ }}} on{\mathbf{ }}|z|{\mathbf{ }}< {\mathbf{ }}1
. We construct a Borel measure and a class of outer measures
h
onH. With these and
h
we show that: (H S)=0 and
h
(H S)=0, (S is the set of normed univalent functions). From
h
(H S)=0 follows—forh=t
—that the Hausdorff—Billingsley-dimension ofH S is zero. |