ENGLISH

I-density continuous functions

By Krzysztof Ciesielski , Lee Larson , Krzysztof Ostaszewski

Book information

Publisher
Amer Mathematical Society
Year
1994
ISBN
9780821825792, 0821825798
Language
english
Format
PDF
Filesize
673 kB (688722 bytes)
Series
Memoirs of the American Mathematical Society
Edition
MemoAMS, AMS
Pages
142\142
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

The classical approach to showing the parallel between theorems concerning Lebesgue measure and theorems concerning Baire category on the real line is restricted to sets of measure zero and sets of first category. This is because classical Baire category theory does not have an analogue for the Lebesgue density theorem. By using ${\mathcal I}$-density, this deficiency is removed, and much of the structure of measurable sets and functions can be shown to exist in the sense of category as well. This monograph explores category analogues to such things as the density topology, approximate continuity, and density continuity. In addition, some questions about topological semigroups of real functions are answered.

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