A New Approach to Universal Measurability

V. Fedorchuk, A. Chizogidze, and T. Banakh in 2003 and V. Bogachev in 2024 posed the following questions: (i) is it true that $P_τ(X)$ is $C$-embedded in $P_σ(X)$; (ii) Is it true that $P_R(X)$ is $C$-embedded in $P_R(βX)$ if and only if $X$ is pseudocompact, where $P_σ$, $P_τ$, and $P_R$ are the fu