Measurability implies continuity for solutions of functional equations - even with few variables |
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Authors: | Antal Járai |
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Institution: | (1) Department of Computer Algebra, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary |
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Abstract: | Summary. We prove that - under certain conditions - measurable solutions $f$ of the functional equation $f(x)=h(x,y,f(g_{1}(x,y)),\ldots,f(g_{n}(x,y))),\quad(x,y)\in D \subset \mathbb{R}^{s} \times \mathbb{R}^{l}$ are continuous, even if $1\le l\le s$. As a tool we introduce new classes of functions which - roughly speaking - interpolate between continuous and Lebesgue measurable functions. Connection between these classes are also investigated. |
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Keywords: | Primary 39B05 Secondary 28A20 28A78 28C15 28E15 04A99 |
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