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Concept
Absolute Continuity
Absolute continuity
is a
stronger form of continuity
for functions, ensuring that the function
preserves the measure of sets
in a
stronger sense than uniform continuity
. It is critical in
real analysis
and
measure theory
, as it guarantees that a function can be represented as the
integral of its derivative
almost everywhere, linking it directly to the
fundamental theorem of calculus
for
Lebesgue integrals
.
Relevant Degrees
Mathematical Analysis 100%
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