On Section Sets of Neighborhoods of Graphs of Semicontinuous Functions

Abstrakt

We prove that for any lower semicontinuous function f:[0,1]->[0,1] with purely unrectifiable graph and for any ε>0 there is an open superset of the graph of f with every vertical section set of one-dimensional Lebesgue measure at most ε.

Klíčová slova

• purely unrectifiable set
• semicontinuous function