Abstract
Let E be a certain nuclear topological vector space contained in the Hilbert space (Z,2) on the real line and let the Gaussian probability measure be defined on the conjugate space E* of E. We consider such a subgroup of the rotation group of (L 2) that acts on E and contains the shift as a one-parameter subgroup. With a rather systematic way we define two more one-parameter subgroups which, together with the shift, constitute a subgroup isomorphic with the projective linear group PGL(2, R). It plays a role of the time change of the white noise. In this set up we formulate and prove the principle of projective invariance of the Brownian motion given by P. Levy.
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