## Nonstandard Methods in Commutative Harmonic Analysis |

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### Contents

Basic concepts of nonstandard analysis | 17 |

31 | 19 |

h | 28 |

fioo | 34 |

Nonstandard analysis of operators acting in spaces of mea | 83 |

Nonstandard analysis on locally compact Abelian groups | 115 |

163 | |

### Common terms and phrases

5-continuous Abelian group arbitrary assertion assumed axiom axiom of separation axiomatics bounded bounded function cardinality consider construct Corollary defined Definition denoted easy elementary extension elements equivalent example exists an internal external finite intersection property finite set function f Gn,jn Haar measure hence homomorphism hyperfinite approximation hyperfinite set hyperfinite-dimensional approximation idealization principle imbedding infinite infinitesimal internal class internal function internal hyperfinite internal set internal set theory internal subsets isomorphism language 31 Lemma lifting linear Loeb measures Loeb space mapping measure space natural numbers nonstandard analysis nonstandard extension nonstandard universe norm notation Obviously operator ordered field predicate proof of Theorem Proposition prove r-standard remark satisfies the conditions semiset sentence sequence set theory standard class standardly finite subgroup subspace Suppose topological space transfer principle ultrafilter unitary zero