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About
characteristic function
(Definition)
Definition
Suppose
is a
subset
of a set
. Then the
function
is the
characteristic function
for
.
Properties
Suppose
are subsets of a set
.
For set
intersections
and set
unions
, we have
For the
symmetric difference
,
For the set
complement
,
Remarks
A synonym for characteristic function is
indicator function
[
1
].
Bibliography
1
G.B. Folland,
Real Analysis: Modern Techniques and Their Applications
, 2nd ed, John Wiley & Sons, Inc., 1999.
"characteristic function" is owned by
bbukh
.
[
full author list
(3) |
owner history
(2) ]
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See Also:
simple function
Other names:
indicator function
Attachments:
examples of characteristic functions
(Example)
by Wkbj79
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Cross-references:
complement
,
symmetric difference
,
unions
,
intersections
,
function
,
subset
There are
40 references
to this entry.
This is
version 7
of
characteristic function
, born on 2001-10-18, modified 2004-11-04.
Object id is
350
, canonical name is
CharacteristicFunction
.
Accessed 17437 times total.
Classification:
AMS MSC
:
03-00
(Mathematical logic and foundations :: General reference works )
26-00
(Real functions :: General reference works )
26A09
(Real functions :: Functions of one variable :: Elementary functions)
28-00
(Measure and integration :: General reference works )
Pending Errata and Addenda
None.
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