2 problems

Positive-measure discontinuity conjecture. The set of discontinuities of $\check{\varrho}$ has positive Lebesgue measure. This is presented as a weaker version of the resist-impuri…

Connected-set continuity conjecture. Condition (2) characterizes continuity: $P$ is continuous if and only if $P(C)$ is connected for every connected subset $C$ of $E$.