Surface measures in infinite-dimensional spaces

We construct surface measures for surfaces of codimensionn≥1 in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous derivative along a subspace. Translated fromMatematickeskie Zametki, Vol. 63, No. 1, pp. 106–114, January, 1998. The author wishes to express his gratitude to V. I. Bogachev for suggesting the problem and for his valuable scientific advice.