International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 809-819

Sublinear functionals ergodicity and finite invariant measures

G. Das1 and B. K. Patel2

1Department of Mathematics, Utkal University, Vani Bihar, Bhubaneswar, Orissa, India
2Department of Mathematics, Khallikote College, Berhampur Pin Code 760001, Orissa, India

Received 21 January 1986

Copyright © 1989 G. Das and B. K. Patel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By introducing a sublinear functional involving infinite matrices, we establish its connection with ergodicity and measure preserving transformation. Further, we characterize the existence of a finite invariant measure by means of a condition involving the above sublinear functional.