TITLE: Dirac delta equality
QUESTION [4 upvotes]: Does the equality below hold?
$$f(x)=\int_{-\infty}^{\infty}f(x')\delta(x-x')dx=\int_{-\infty}^{\infty}f(x')\delta(x'-x)dx$$

REPLY [0 votes]: Yes since the argument of the delta distribution equals zero when x=x' in either case, and the result is f(x) for either integral, assuming dx is changed to dx'.
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