Why is the support of Dirac distribution $\{0\}$? Distributions are of two types: those that are obtained from locally integrable functions, and those that aren't. For the first type, the support of distribution is simply the support of the function. For the other kind of distribution, for example, the Dirac Delta 'function', we can't find the support this way. 

The support of the Dirac Delta distribution is given to be the set $\{0\}$. Can someone help me in understanding why?
Well the definition of the support is defined as the part of the domain where the distribution is non-zero. There are a few definitions of the Dirac delta but all agree that $x\neq 0 \implies \delta(x) = 0$.
Well the definition of the support is defined as the part of the domain where the distribution is non-zero. There are a few definitions of the Dirac delta but all agree that $x\neq 0 \implies \delta(x) = 0$.