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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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Convergence of ODE with uniform $L^\infty \cap L^1$ bound on nonlinearity

Consider the IVP $$ \left\{ \begin{aligned} \frac{d}{dt} \Phi_n(t,x) &= f_n(\Phi_n(t,x)) && \forall t \in \mathbf{R}_+ \\ \Phi_n(0,x) &= x && \forall x \in \mathbf{R} \end{aligned}\right. $$ for $n \i …
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