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${\mathcal I}$-Density Continuous Functions

Available Formats:
Electronic ISBN: 978-1-4704-0092-7
Product Code: MEMO/107/515.E
List Price: $40.00 MAA Member Price:$36.00
AMS Member Price: $24.00 Click above image for expanded view${\mathcal I}$-Density Continuous Functions Available Formats:  Electronic ISBN: 978-1-4704-0092-7 Product Code: MEMO/107/515.E  List Price:$40.00 MAA Member Price: $36.00 AMS Member Price:$24.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1071994; 133 pp
MSC: Primary 26; Secondary 28;

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.

Research mathematicians.

• Chapters
• 1. The ordinary density topology
• 2. Category analogues of the density topology
• 3. $\mathcal {I}$-density continuous functions
• 4. Semigroups
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Volume: 1071994; 133 pp
MSC: Primary 26; Secondary 28;

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.

• 3. $\mathcal {I}$-density continuous functions