Definition:Lebesgue Integral/Notation

Lebesgue Integral: Also known as

The Lebesgue integral is frequently abbreviated as $\ds \int_E \phi$ or just $\ds \int \phi$.

If $E$ is the closed interval $\closedint a b$, we frequently write:

$\ds \int_a^b f = \int_E f$

Historically, the notations $\ds \int \map f x \rd x$ and $\ds \int f \rd x$ are used for the Lebesgue integral in place of the formally correct $\ds \int f \rd \lambda^n$.

Sources

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• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 10$