On Absolutely Continuous Transformations

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

NONINVERTIBLE TRANSFORMATIONS ADMITTING NO ABSOLUTELY CONTINUOUS ct-FINITE INVARIANT MEASURE

We study a family of H-to-1 conservative ergodic endomorphisms which we will show to admit no rj-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as C°° endomorphisms of the 2-torus.

A general spline representation for nonparametric and semiparametric density estimates using diffeomorphisms

A theorem of McCann [15] shows that for any two absolutely continuous probability measures on Rd there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that density estimation can be recast in terms of transformations. In particular, one can fix any absolutely continuous probability measure, call it P, and t...

On Essentially Absolutely Continuous Plane Transformations

ON THE EXISTENCE OF INVARIANT MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS ( l ) BY A . LASOTA AND

A class of piecewise continuous, piecewise C transformations on the interval [O, l] is shown to have absolutely continuous invariant measures.