Glossary

{ }: a collection of points satisfying some property, e.g. { r : r ? a} is the collection of all real numbers less than or equal to a value a
[ ]: an interval of real points including the end points, e.g. for a ? b [ a, b] = { r : a ? r ? b}. Called a closed interval
( ): an interval of real points excluding the end points, e.g. for a ? b ( a, b) = { r : a < r < b}. Called an open inter val. Note this is empty if a = b
( ], [ ): denote intervals of real points including one endpoint and excluding the other, e.g. for a ? b ( a, b] = { r : a < r ? b} [ a, b) = { r : a ? r < b}
: the empty set, the set that contains no points.,
: for all
?: the sample space or universal set, the set that contains all of the points
#( F): the number of elements in a set F
: equal by definition
exp: the exponential function, exp( x) e ^x, used for clarity when x is complicated
: sigma-field or event space
( ?

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An Introduction to Statistical Signal Processing