# Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

Formalized Mathematics (2008)

- Volume: 16, Issue: 3, page 283-288
- ISSN: 1426-2630

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topYatsuka Nakamura, and Hisashi Ito. "Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences." Formalized Mathematics 16.3 (2008): 283-288. <http://eudml.org/doc/266669>.

@article{YatsukaNakamura2008,

abstract = {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 a 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 (see [7]) and it is the preparation for its proof.},

author = {Yatsuka Nakamura, Hisashi Ito},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {283-288},

title = {Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences},

url = {http://eudml.org/doc/266669},

volume = {16},

year = {2008},

}

TY - JOUR

AU - Yatsuka Nakamura

AU - Hisashi Ito

TI - Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

JO - Formalized Mathematics

PY - 2008

VL - 16

IS - 3

SP - 283

EP - 288

AB - 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 a 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 (see [7]) and it is the preparation for its proof.

LA - eng

UR - http://eudml.org/doc/266669

ER -

## References

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- [13] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
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