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The restriction of an isotropic α-stable Lévy process  X  α  in ℝ  n   on the fractal support  F  of certain finite Borel measures μ is introduced in three different ways: by means of the trace of its Dirichlet form on  F  and related Besov spaces, by its μ-local time on  F  and the corresponding time changed process, and by restricting on the fine support of μ via balayage spaces and potentials.

Restricting isotropic α-stable Lévy processes from to fractal sets