# absolutely continuous function

## absolutely continuous function

[¦ab·sə‚lüt·lē kən¦tin·yə·wəs ′fəŋk·shən] (mathematics)

A function defined on a closed interval with the property that for any positive number ε there is another positive number η such that, for any finite set of nonoverlapping intervals, (

*a*_{1},*b*_{1}), (*a*_{2},*b*_{2}), … , (*a*,_{n}*b*), whose lengths have a sum less than η, the sum over the intervals of the absolute values of the differences in the values of the function at the ends of the intervals is less than ε._{n}McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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