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I'm reading the probabilistic book write by çinlar, but I don't understand the Kernel theory, in details: $ (E,\mathcal{E}),(F,\mathcal{F})$ are two measurable space $$K:E \times \mathcal{F} \rightarrow R_{+}$$ with these proprieties: they are measurable on $E$ fixed $B\in\mathcal{F}$, and they are a measure on $F$ fixed $x\in E$. After this definitio the book present the following operation between Kernels and functions: $$Kf(x)=\int_{F}K(x,dy)f(y)$$ But what does $K(x,dy)$ mean? in the theory of measure i haven't see nothing simalar, how one can calculate this integrals with the strange $dy$ (that I think means lebesgue measure)?

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I've resolved! since the kernel is a measure fixed $x$ I can integrate the function $f$ respect to this measure (notation $\nu(dx)$ means integrate respet to measure $\nu$ and variables $x$)!

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