For a non-negative nondecreasing unbounded continuous on the right function $F$ and a real-valued function $f$  on  $(1,+\|)$ the integral $I(\s)=\int_{1}^{\|}f(x)e^{x\s}dF(x)$ is called the Laplace-Stieltjes integral. For some class of such integrals three various topologies  are introduced and their equivalence is proven.

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