### Abstract

An infinite matrix is said to be doubly substochastic if it has nonnegative components and each row and each column sum is at most 1. Let x and y be two real sequences which converge to 0 or which are absolutely summable. This paper introduces necessary and sufficient conditions for existence of an infinite doubly substochastic matrix A such that x=Ay concerning partial order and convex hull for sequences.

Original language | English |
---|---|

Pages (from-to) | 119-128 |

Number of pages | 10 |

Journal | Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete |

Volume | 61 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1982 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

**On infinite doubly substochastic matrices.** / Komiya, Hidetoshi.

Research output: Contribution to journal › Article

*Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete*, vol. 61, no. 1, pp. 119-128. https://doi.org/10.1007/BF00537229

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TY - JOUR

T1 - On infinite doubly substochastic matrices

AU - Komiya, Hidetoshi

PY - 1982/3

Y1 - 1982/3

N2 - An infinite matrix is said to be doubly substochastic if it has nonnegative components and each row and each column sum is at most 1. Let x and y be two real sequences which converge to 0 or which are absolutely summable. This paper introduces necessary and sufficient conditions for existence of an infinite doubly substochastic matrix A such that x=Ay concerning partial order and convex hull for sequences.

AB - An infinite matrix is said to be doubly substochastic if it has nonnegative components and each row and each column sum is at most 1. Let x and y be two real sequences which converge to 0 or which are absolutely summable. This paper introduces necessary and sufficient conditions for existence of an infinite doubly substochastic matrix A such that x=Ay concerning partial order and convex hull for sequences.

UR - http://www.scopus.com/inward/record.url?scp=34250231585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250231585&partnerID=8YFLogxK

U2 - 10.1007/BF00537229

DO - 10.1007/BF00537229

M3 - Article

AN - SCOPUS:34250231585

VL - 61

SP - 119

EP - 128

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -