Davar Khoshnevisan
Published 2004-06-28Version 1
We present a self-contained and modern survey of some existing quasi-sure results via the connection to the Brownian sheet. Among other things, we prove that quasi-every continuous function: (i) satisfies the local law of the iterated logarithm; (ii) has Levy's modulus of continuity for Brownian motion; (iii) is nowhere differentiable; and (iv) has a nontrivial quadratic variation. We also present a hint of how to extend (iii) to obtain a quasi-sure refinement of the M. Csorgo--P. Revesz modulus of continuity for almost every continuous function along the lines suggested by M. Fukushima.
Comments: 23 pages. Proceedings of the Fields Institute (to appear)
Brownian sheet and time inversion -- From $G$-orbit to $L(G)$-orbit
Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces
On the distribution of maximum of a Brownian sheet restricted to a lower-dimensional set
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