Oxford

I will present a new formula for diffusion processes which involving

Ito integral for the transition probability functions. The nature of

the formula I discovered is very close to the Kac formula, but its

form is similar to the Cameron-Martin formula. In some sense it is the

Cameron-Martin formula for pinned diffusions.

Marstrand's Theorem is a one of the classic results of Geometric Measure Theory, amongst other things it says that fractal measures do not have density. All methods of proof have used symmetry properties of Euclidean space in an essential way. We will present an elementary history of the subject and state a version of Marstrand's theorem which holds for spaces whose unit ball is a polytope.