Kernel Transformation of Measure is Measure
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Theorem
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.
Let $N: X \times \Sigma \to \overline{\R}_{\ge0}$ be a kernel.
Then $\mu N: X \to \overline{\R}$, the kernel transformation of $\mu$, is a measure.
Proof
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Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 9$: Problem $11 \ \text{(i)}$
