  L.Accardi shows that the Banach space of singed measures is homeomorphic to
the Hilbert space formed by so-called root measures. In this paper, we redefine
root measures in view of the theory of measures on infinite dimensional spaces,
and introduce a notion of differentiation, Fourier transform, and convolution
product for root measures, and examine those relations. We also study about
L\'{e}vy Laplacian on Wiener space as application. It is shown that the symbol
of L\'{e}vy Laplacian is equal to the quadratic variation of paths.
