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A 0–1 law for multiplicative functional equations

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The 0–1 principle stating that for the multiplicative functional equation

$$\prod_{i=1}^m f_i(x_i)=\prod_{j=1}^n g_j(y_j)$$

satisfied almost everywhere one of the unknown functions \({f_{i}}\)’s and \({g_{j}}\)’s is zero almost everywhere on both sides or all of them are nonzero almost everywhere is generalized for functions defined on connected manifolds \({X_{i}}\)’s and \({Y_{j}}\)’s (the \({y_{j}}\)’s are given functions). Corollaries proving that the unknown functions are almost equal to nowhere zero \({\mathcal{C}^{\infty}}\) functions satisfying the functional equation everywhere are also given. The Baire category analogues is also treated.

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  1. Dieudonné, J.: Grundzüge der modernen Analysis. VEB Deutscher Verlag der Wissenschaften I.-IX., 1985–1987

  2. Federer H.: Geometric Measure Theory. Springer, Berlin (1969)

    MATH  Google Scholar 

  3. Geiger D., Heckerman D.: A characterization of the Dirichlet distribution through global and local parameter Independence. Ann. Stat. 25, 1344–1369 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Járai A.: Regularity property of the functional equation of the Dirichlet distribution. Aequat. Math. 58, 37–46 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Járai A.: Regularity Properties of Functional Equations in Several Variables. Springer, New York (2005)

    MATH  Google Scholar 

  6. Járai A.: Regularity properties of measurable functions satisfying a multiplicative type functional equation almost everywhere. Aequat. Math. 89, 367–381 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Járai A., Lajkó K., Mészáros F.: On measurable functions satisfying multiplicative type functional equations almost everywhere. In: Bandle, C., Gilányi, A., Losonczi, L., Plum, M. (eds.) Inequalities and Applications, vol. 161., Birkhäuser, Basel (2012)

    Google Scholar 

  8. Mészáros F., Lajkó K.: Functional Equations and Characterization Problems. WDM Verlag, New York (2011)

    MATH  Google Scholar 

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Correspondence to Antal Járai.

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Dedicated to Professor Roman Ger to his 70th birthday

This work has been supported by OTKA K111651 grant.

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Járai, A. A 0–1 law for multiplicative functional equations. Aequat. Math. 90, 147–161 (2016).

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