### Abstract

I shall discuss several problems which are connected with the Scottish Book. Let me start with a problem which F.Bagemihl and I solved. Everybody knows Riemann’s theorem: A nonabsolutely convergent series of real numbers has the property that for any preassigned numbera the series can be reordered to converge toa. Bagemihl and I proved that for the Cesàro sum of the series there are three possibilities: On reordering the domain of convergence is just one point or it is the whole line, or it is an arithmetic progression (this last possibility does not occur in Riemann’s theorem). Our paper appeared inActa Mathematicain 1954; later we found that it is Problem28 of the Scottish Book, due to Mazur.

Original language | English |
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Title of host publication | The Scottish Book: Mathematics from the Scottish Cafe, with Selected Problems from the New Scottish Book, Second Edition |

Publisher | Springer International Publishing |

Pages | 27-33 |

Number of pages | 7 |

ISBN (Print) | 9783319228976, 9783319228969 |

DOIs | |

Publication status | Published - Jan 1 2015 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*The Scottish Book: Mathematics from the Scottish Cafe, with Selected Problems from the New Scottish Book, Second Edition*(pp. 27-33). Springer International Publishing. https://doi.org/10.1007/978-3-319-22897-6_4