Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (
), it is used as a symbol for sums
and series.
As a lower case letter (
) it is a prefix used in several
contexts to indicate that a term is referred in some way to countable unions. For
example, a sigma-algebra is a collection of sets
closed under countable union and a sigma-compact
topological space is a topological space
which is the union of countably many compact subsets. The symbol 
is also used to denote the divisor
function.
Another common usage of the symbol 
is to denote the standard
deviation (i.e., square root of the variance) of
a statistical distribution. However, some care is needed in interpreting the meaning
of 
, since this symbol is also commonly used as a parameter
related to but not equivalent to the square root of the variance, for example in
the log normal distribution, Maxwell
distribution, and Rayleigh distribution.
