Measure of Dirac

A measurement of Dirac or mass of Dirac is a measurement supported by a singleton and of total mass 1. More precisely, for a measurable Space $(X,\; \backslash \; Omega)$ and a point has X , one calls measurement of Dirac at the point $a$ the measurement, generally noted $\backslash \; delta\_a$, on $(X,\; \backslash \; Omega)$ such as:

$\backslash \; forall\; has\; \backslash \; in\; \backslash \; Omega,\; (\backslash \; delta\_a\; (A)=1\; \backslash ;\; \backslash \; textrm\; \{if\}\; \backslash ;\; has\; \backslash \; in\; has\; \backslash ;\; \backslash \; textrm\; \{and\}\; \backslash ;$

\ delta_a (A)=0 \; \ textrm {if} \; \ notin A) has. The support of $\backslash \; delta\_a$ is tiny room to the singleton $\backslash \; \{has\; \backslash \}$.

The masses of Dirac are not alleviating measurements: they have a practical utility. They make it possible for example to build measurements by successive approximations.

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