Almost everywhere means at all points except possibly those in a set of measure zero . More precisely, let measure space .
A property holds almost everywhere on measurable
set
For example, two measurable functions are
equal almost everywhere if
Changing a function on a set of measure zero therefore does not change statements
made only almost everywhere. The corresponding terminology for a probability
measure is almost surely .
See also Almost Everywhere Convergence ,
Almost Surely ,
Measure
Zero
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References Jeffreys, H. and Jeffreys, B. S. "'Measure Zero': 'Almost Everywhere.' " §1.1013 in Methods
of Mathematical Physics, 3rd ed. Sansone, G. Orthogonal
Functions, rev. English ed. Referenced
on Wolfram|Alpha Almost Everywhere
Cite this as:
Weisstein, Eric W. "Almost Everywhere."
From MathWorld https://mathworld.wolfram.com/AlmostEverywhere.html
Subject classifications
be a measure space.
A property holds almost everywhere on 
if it holds on a measurable
set 
for which 
.
