Research Communication | Open Access
Volume 2021 | Communication ID 289
Volume 2021 | Communication ID 289
| On the partition theorem of the excessive functions via integral representation |
Abderrahim Aslimani
Received |
Accepted |
Published |
February 05, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: Brelot in [3] established in a P-harmonic space Ω (i.e., admitting a potential strictly positive) as part of his axiomatic that, if A is any subset of Ω and u is a positive superharmonic function, then u=u_1+u_2, where u_1=R ̂_(u_1)^A and u_2=R ̂_(u_2)^A, with uniqueness of this decomposition if we impose to u_2 (respectively u_1) to be the specific greatest minorant of u which is autoreduite on Ω∖A (respectively on A). Our aim in the present work is to establish the Brelot partition theorem in any measurable space (E,ℇ) for the excessive functions which are finite ...