On the mathematics behind the Dyson Series

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I've come across the Dyson Series solution of the Schrödinger Equation arising in the interaction picture when dealing with a time dependent Hamiltonian. Since then I've been looking for a rigorous definition of the integral of operators which appears repeatedly in the formula but I didn't find much. Is there perhaps a general theory of this type of integrals? Or is it just a formal definition whose meaning I've not understood? Anyhow I'd appreciate very much if you could suggest any reference about the topic. Thank you in advance for the answer.