Change of variable formulas for integrals over superspaces

A study was conducted to demonstrate change of variable formulas for integrals over subspaces. The majority of results of the study were related to the observation that formulas describing transformation of measures on vector spaces generated by transformations of these spaces were extended to transformations of supermeasures on superspaces. These spaces were extended to transformations of supermeasures on superspaces by replacing the (infinite) determinants in these formulas by superdeterminants and operations of supermeasures obtained were useful in studying quantum anomalies. The study also considered similar formula for transformations of the Feynman Hamiltonian pseudomeasure and discussed the possibility of obtaining such formulas by using generalized densities of measures and their superanalogues.