An example on null sets of parabolic measures
Jang-Mei Gloria Wu · Proceedings of the American Mathematical Society · 1989
A set E E on the real line of Hausdorff dimension 1 is constructed, such that the graph of E E on the boundary of any C 2 {C^2} domain { t > τ ( x ) } \left \{ {t > \tau (x)} \right \} , or on the boundary of any Lip 1 2 {\text {Lip}}\tfrac {1}{2} domain { x > χ ( t ) } \left \{ {x > \chi (t)} \right \} , is null with respect to the parabolic measure associated with any parabolic operator L = a ( x , t ) ∂ 2 / ∂ x 2 − ∂ / ∂ t L = a(x,t){\partial ^2}/\partial {x^2} - \partial /\partial t on R 2 ; a {{\mathbf {R}}^2};a is Hölder continuous and 0 >