@MISC{AFINSQ_2.MIZ,
  AUTHOR = {Nakamura, Yatsuka and Ito, Hisashi},
  TITLE = {Basic Properties and Concept of Selected Subsequence
    of Zero Based Finite Sequences},
  SECTION1 = {Preparation},
  SECTION2 = {Additional Properties of Zero Based Finite Sequence},
  SECTION3 = {Selected Subsequences},
  DAY = {27},
  MONTH = {June},
  YEAR = {2008},
  ADDRESS1 = {Shinshu University},
  ADDRESS2 = {Shinshu University},
  SUMMARY = {Here, we develop the theory of zero based finite sequences,
  which are, sometimes, more useful in applications than normal one based
  finite sequences.
  The fundamental function Sgm is introduced as well as in case of
  normal finite sequences and other notions are also introduced.
  However many theorems are modification of old theorems of normal
  finite sequences, they are basically important and are necessary
  for applications.
  A new concept of selected subsequence is introduced. This concept
  came from the individual Ergodic theorem (\cite{Halmos:1956}) and it is
  the preparation for its proof.}}

@BOOK{Halmos:1956,
       AUTHOR = {Paul R. Halmos},
        TITLE = {Lectures on Ergodic Theory},
    PUBLISHER = {The Mathematical Society of Japan},
         YEAR = {1956},
         NOTE = {No.3}}

