Smooth measures on loop groups (Q1374939)

Smooth measures on groups of mappings of a segment or a circumference into a (compact) Lie group are defined as surface measures that are induced by embeddings of these groups into vector spaces of functions (on a segment or a circumference) with values in spaces of matrices of a sufficiently high dimension that are equipped with the Wiener measure or any other smooth measure. This method allows one to reduce the investigation of differential properties and properties of measures on such groups close to them to the investigation of similar properties of measures on vector spaces. In this note, we use this method to find logarithmic derivatives of measures (on groups of mappings of a segment or a circumference into a compact Lie group) and to obtain an analog of the Maruyama-Girsanov-Ramer formula.