This paper considers the following question: Given an Anosov endomorphism f on T~m, whether f is topologically conjugate to some hyperbolic total endomorphism?
The following result is established:let X be a Banach space without the Radon-Nikodym property,there exists a uniformly bounded harmonic function f defined onth
Let be the collection of m-times continuously differentiable probability densities fon R<sup>d</sup> such that 丨D<sup>a</sup>f(x<sub>1</sub>)-D<sup>a</sup>f(x<su