What is the Dirac mass on measure space?

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I am reading the book "Lectures on Stochastic Analysis." But I know seldom about measure space. I meet with a symbol which the author call Dirac mass(in 9.3 of this book). Let E be a measurable space, $x\in E$, $\delta_{x}$ is the Dirac mass at x. So what is Dirac mass on a measurable space.