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| The existence of strong solutions for stochastic delay inclusion $dx(t)\in F(t,x_t)dt+G(t,x_t)dW(t)$, $x_0=\xi$ will be discussed for measurable multifunctions $F,G:\;[0,T]\times C(-r,0)\rightarrow ClConvR^n$ being upper separated with respect to their second variable. The result will follow by the Carath\'eodory type selection method. Therefore, the problem of the existence of Carath\'eodory-convex selections in nonseparable Banach spaces for multifunctions of the type mentioned above will be discussed in detail. |
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