Symmetric Difference On Measure Spaces
As long as there is a notion of "how big" a set is, the symmetric difference between two sets can be considered a measure of how "far apart" they are. Formally, if μ is a σ-finite measure defined on a σ-algebra Σ, the function,
is a pseudometric on Σ. d becomes a metric if Σ is considered modulo the equivalence relation X ~ Y if and only if . The resulting metric space is separable if and only if L2(μ) is separable.
Read more about this topic: Symmetric Difference
Famous quotes containing the words difference, measure and/or spaces:
“The greater intellect one has, the more originality one finds in men. Ordinary persons find no difference between men.”
—Blaise Pascal (1623–1662)
“Perpetual modernness is the measure of merit in every work of art.”
—Ralph Waldo Emerson (1803–1882)
“We should read history as little critically as we consider the landscape, and be more interested by the atmospheric tints and various lights and shades which the intervening spaces create than by its groundwork and composition.”
—Henry David Thoreau (1817–1862)