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Let $C = C([a,b],\mathbb{R}^n)$ be a space of continuous vectorvalued functions on $[a,b]$. Let $y \in C$, $\Phi \in C^*$ and $f \in C(\mathbb{R}^n, \mathbb{R}^n)$. What does mean a notation $ A = \int\limits_{a}^{b} f(d\Phi(t))^{T} y(t) $ If $\Phi \in C^{1}([a,b],\mathbb{R}^n)$ then $ A = \int\limits_{a}^{b} f(\Phi'(t))^{T}y(t)dt, $ but in general case I'm confused.

Another example of use of similar notation is further: $ \int\limits_{a}^{b} \delta^{*}(d\Phi(t) \mid M(t)) $ Here $\delta^{*}(\cdot \mid M(t))$ is a support function for the set $M(t)$.

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    Un$f$ortunately I can't give a reference, but I can update my question with a particular example.2012-06-05

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