| Abstrakt: |
An integral (1.1.1) is said to be in parametric form, and we say f is the integrand of a parametric problem, if and only if the value of the integral is unchanged by an arbitrary diffeomorphism with positive Jacobian from G onto another domain G'; if we assume that f (x, z, p) is defined everywhere, we see that we must have (9.1.1) ]> for any G', and vector z'ϵ C1( ]> ), and any positive diffeomorphism x' = x' (x) from ]> onto G'. By taking x0, z0, 'p, and x0' as arbitrary constants and defining (9.1.2) ]> and taking G = B (x0, ρ) and then letting ρ → 0, we obtain (9.1.3) ]> for all sets of constants as indicated. Thus, f must be independent of x and we must have N ≥ v. [ABSTRACT FROM AUTHOR] |
