Integration on Lie supergroups. A Hopf superalgebra approach

For a large class of finite-dimensional Lie superalgebras (including the classical simple ones) a Lie supergroup associated to the algebra is defined by fixing the Hopf superalgebra of functions on the supergroup. Then it is shown that on this Hopf superalgebra there exists a non-zero left integral. According to a recent work by the authors, this integral is unique up to scalar multiples.