Kronecker delta
Notable properties

The Kronecker delta has the so-called sifting property that for j ∈ Z {\displaystyle j\in \mathbb {Z} }:

and if the integers are viewed as a measure space, endowed with the counting measure, then this property coincides with the defining property of the Dirac delta function

and in fact Dirac's delta was named after the Kronecker delta because of this analogous property. In signal processing it is usually the context (discrete or continuous time) that distinguishes the Kronecker and Dirac "functions". And by convention, δ (t) {\displaystyle \delta (t)} generally indicates continuous time (Dirac), whereas arguments like i {\displaystyle i}, j {\displaystyle j}, k {\displaystyle k}, l {\displaystyle l}, m {\displaystyle m}, and n {\displaystyle n} are usually reserved for discrete time (Kronecker). Another common practice is to represent discrete sequences with square brackets; thus: δ {\displaystyle \delta }. The Kronecker delta is not the result of directly sampling the Dirac delta function.

The Kronecker delta forms the multiplicative identity element of an incidence algebra.
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