# fa.practical evaluation – Is the pointwise supremum of a steady responsibility steady? retort

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## fa.practical evaluation – Is the pointwise supremum of a steady responsibility steady?

Suppose $$f(x , y)$$ is steady in each variables. For any $$epsilon > 0$$ and a few $$y_0$$, let $$h_{epsilon}(x) = max_{y^{‘}: | y^{‘} – y_0 | leq epsilon} f(x , y^{‘})$$. It appears to me that $$h_{epsilon}(x)$$ is steady in $$epsilon$$ on $$(0 , infty)$$, that’s, for any $$epsilon_n rightarrow epsilon_0 > 0$$, one has $$h_{epsilon_n}(x) rightarrow h_{epsilon_0}(x)$$.

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