Some articles on measure theory, theory, measure, measures:
... Many of the formulas in information theory have separate versions for continuous and discrete cases, i.e ... These versions can often be generalized using measure theory ... can be considered density functions with respect to the counting measure, thus requiring only basic discrete mathematics for what can be considered, in a measure theory context, integration ...
... In mathematics, geometric measure theory (GMT) is the study of the geometric properties of the measures of sets (typically in Euclidean spaces), including such things as arc lengths and areas ... It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets ... Deep results in geometric measure theory identified a dichotomy between rectifiable sets on the one hand and purely unrectifiable or fractal sets on the other ...
... To define the Hellinger distance in terms of measure theory, let P and Q denote two probability measures that are absolutely continuous with respect to a third ... distance between P and Q does not change if λ is replaced with a different probability measure with respect to which both P and Q are absolutely continuous ...
Famous quotes containing the words theory and/or measure:
“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (182595)
“The measure of the little while
That Ive been long away.”
—Robert Frost (18741963)