Uniform absolute continuity
Encyclopedia
In mathematical analysis
, a collection of real
-valued and integrable functions is uniformly absolutely continuous, if for every
there exists
such that for any measurable set , implies
for all .
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, a collection of real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
-valued and integrable functions is uniformly absolutely continuous, if for every
there exists
such that for any measurable set , implies
for all .