## Abstract

We construct a variety of mappings from the unit interval I into L^{p}([0,1]); 1 ≤ p >^{ ∞} to generalize classical examples of L^{p}-converging equences of functions with simultaneous pointwise divergence. By es-tablishing relations between the regularity of the functions in the image of the mappings and the topology of I, we obtain examples which are L^{p}-continuous but exhibit discontinuity in a pointwise sense to different egrees. We conclude by proving a Lusin-type theorem, namely that if almost every function in the image is continuous, then we can remove a set of arbitrarily small measure from the index set I and establish pointwise continuity in the remainder.

Original language | English |
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Pages (from-to) | 177-192 |

Number of pages | 16 |

Journal | Real Analysis Exchange |

Volume | 38 |

Issue number | 1 |

Publication status | Published - 2013 |