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The existence of a maximal “cross-sectional” filter on the Boolean algebra of measurable sub...

No. Suppose $\mathcal{F}$ is such a filter. Clearly each $X \in \mathcal{F}$ has positive measure intersection with every positive-length interval. Then neither $[0,1/2]$ nor $[1/2, 1]$ are in the fil …
Elliot Glazer's user avatar