## Encyclopaedia of Mathematics, Volume 6This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques. |

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### Contents

Section 1 | 1 |

Section 2 | 10 |

Section 3 | 44 |

Section 4 | 54 |

Section 5 | 58 |

Section 6 | 64 |

Section 7 | 65 |

Section 8 | 96 |

Section 16 | 204 |

Section 17 | 251 |

Section 18 | 276 |

Section 19 | 278 |

Section 20 | 292 |

Section 21 | 301 |

Section 22 | 306 |

Section 23 | 309 |

Section 9 | 120 |

Section 10 | 126 |

Section 11 | 138 |

Section 12 | 142 |

Section 13 | 153 |

Section 14 | 164 |

Section 15 | 166 |

Section 24 | 316 |

Section 25 | 365 |

Section 26 | 376 |

Section 27 | 378 |

Section 28 | 381 |

Section 29 | 387 |

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### Common terms and phrases

1980 Subject Classification Acad algebra algorithm Amer AMS 1980 Subject analysis analytic approximation axiom Banach space calculus called coefficients compact complete computational construction convergence corresponding curvature curve defined denoted differential equations distribution domain Editorial comments eigen elements equivalent ergodic Euclidean Euclidean space example field finite formula func function geometry given homomorphism ideal integral isomorphic Lie algebras linear operators locally convex locally convex space logic Luzin Lyapunov Mal'tsev algebras manifold mapping Markov chain Math mathematical matrix measure meromorphic meromorphic function method metric space minimal surfaces module Moscow natural numbers Nauk neighbourhood nilpotent Noetherian non-linear norm normal obtained optimal control parameters plane polynomial properties real numbers References A1 Riemann ring Russian satisfies semi-group sequence solution Springer statistical stochastic structure subgroup subset theorem tion topological space topology transformation translated Univ vector space zero