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Miklós Schweitzer 2012 P8

Source: Miklós Schweitzer 2012 P8

August 20, 2018
college contestsMiklos Schweitzer

Problem Statement

For any function f:R2→Rf: \mathbb{R}^2\to \mathbb{R} consider the function Φf:R2→[−∞,∞]\Phi_f:\mathbb{R}^2\to [-\infty,\infty] for which Φf(x,y)=lim sup⁡z→yf(x,z)\Phi_f(x,y)=\limsup_{ z \to y} f(x,z) for any (x,y)∈R2(x,y) \in \mathbb{R}^2.
[*]Is it true that if ff is Lebesgue measurable then Φf\Phi_f is also Lebesgue measurable?[/*] [*]Is it true that if ff is Borel measurable then Φf\Phi_f is also Borel measurable?[/*]
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