## Encyclopedia of Physical Science and Technology, Volume 1 |

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Page 506

In this approach we try to prove that a specific sentence, in the language ii, is not

a

would be able to establish the consistency of some theories having only infinite ...

In this approach we try to prove that a specific sentence, in the language ii, is not

a

**theorem**by reasoning in the metalanguage. It was Hilbert's hope that onewould be able to establish the consistency of some theories having only infinite ...

Page 515

Their

large that if the set S„(k) of all k- member subsets of the set S„ of integers such

that 1 s x s n is partitioned into r disjoint sets (i.e., S„(k) = Z, U Z2 U ••□ U Zr, Z, fl Z

, ...

Their

**theorem**states that given any positive integers k, r, and s, there is an n solarge that if the set S„(k) of all k- member subsets of the set S„ of integers such

that 1 s x s n is partitioned into r disjoint sets (i.e., S„(k) = Z, U Z2 U ••□ U Zr, Z, fl Z

, ...

Page 545

We come now to the main

convergence

such that |/„| S g where g is integrable and if lim/„ = /a.e. then /is integrable and

Another ...

We come now to the main

**theorem**of this section: Lebesgue's dominatedconvergence

**theorem**. It states that if {/„} is a sequence of measurable functionssuch that |/„| S g where g is integrable and if lim/„ = /a.e. then /is integrable and

Another ...

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#### Encyclopedia of physical science and technology

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### Contents

Liquid Alkali Metals 1 John F Schenck | 337 |

Liquid Chromatography 13 Russell L Rasmussen Joseph | 363 |

Liquid Crystal Devices 41 Manifold Geometry | 397 |

Copyright | |

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