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- W2007364048 abstract "Let Ω be a set and Ω1, . . . , Ω m−1 subsets of Ω, being m an integer greater than one. For a given function ({f = (f_1,ldots f_m) : Omega rightarrow mathbb{R}^m}), we prove the existence of a unique function ({alpha = (alpha_1,ldots,alpha_m) : Omega rightarrow mathbb{R}^m}) such that$${left{begin{array}{lll}{qquad qquad quad alpha_i ,=,alpha_{i+1}quad{rm on} ; Omega_i} {alpha_1+cdots+alpha_i , = , f_1+cdots+f_iqquad {rm on}; OmegasetminusOmega_i, quad{rm for, all}; i < m} {alpha_1+cdots+alpha_m , = , f_1+cdots+f_m,}end{array}right.}$$called the average function of ({f : Omega rightarrow mathbb{R}^m}) relatively to (Ω, Ω1, . . . , Ω m−1). When Ω is a topological space and f is a continuous function, we find necessary and sufficient conditions for the continuity of the average function of f. We write α i as a linear combination of characteristic functions of the (coincidence) sets ({cap_{j=r}^sOmega_j}), 1 ≤ r ≤ s ≤ m − 1, belonging the coefficients to ({mathbb{Q}[f_1, . . . ,f_m]})." @default.
- W2007364048 created "2016-06-24" @default.
- W2007364048 creator A5003160523 @default.
- W2007364048 date "2011-08-10" @default.
- W2007364048 modified "2023-09-24" @default.
- W2007364048 title "Characteristic functions and averages" @default.
- W2007364048 cites W2117636580 @default.
- W2007364048 doi "https://doi.org/10.1007/s13370-011-0040-z" @default.
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