I-Density Continuous Functions (Memoirs of the American Mathematical Society)
( Memoirs of the American Mathematical Society )
Publication series ：Memoirs of the American Mathematical Society
Author： Krzysztof Ciesielski
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470400927
P-ISBN(Paperback): 9780821825792
Subject： O174.1 Real, real function
Keyword： Analysis
Language： ENG
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I-Density Continuous Functions (Memoirs of the American Mathematical Society)
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.