On measurable polynomials on infinite-dimensional spaces. (English. Russian original) Zbl 1275.28002
Dokl. Math. 87, No. 2, 214-217 (2013); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk, Vol. 449, No. 6, 627-630 (2013).
The authors describe the contents of this paper as follows. “We prove the existence of a polynomial in the usual sense of measurable polynomials on infinite-dimensional spaces with measures. A similar assertion is proved for a broad class of measurable polylinear functions.” ... “ The main result of this paper gives a polynomial extension of a function that is the point-wise limit of a sequence of polynomials of degree \(d\) on the set of all points of convergence of this sequence.”
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 28A20 | Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
References:
| [1] | Wiener, N., No article title, Am. J. Math., 60, 879-936 (1938) · JFM 64.0887.02 |
| [2] | V. I. Bogachev, Gaussian Measures (Am. Math. Soc., Providence, RI, 1998). · Zbl 0913.60035 |
| [3] | V. I. Bogachev, Differentiable Measures and the Malliavin Calculus (Am. Math. Soc., Providence, RI, 2010). · Zbl 1247.28001 |
| [4] | V. I. Bogachev, O. G. Smolyanov, and V. I. Sobolev, Topological Vector Spaces and Their Applications (RKhD, Moscow, 2012) [in Russian]. · Zbl 1378.46001 |
| [5] | Agafontsev, B. V.; Bogachev, V. I., No article title, Dokl. Math., 80, 806-809 (2009) · Zbl 1195.60054 · doi:10.1134/S1064562409060064 |
| [6] | G. E. Shilov and Fan Dyk Tin’, Integral, Measure, and Derivative on Linear Spaces (Nauka, Moscow, 1967) [in Russian]. · Zbl 0162.19002 |
| [7] | Smolyanov, O. G., No article title, Sov. Math. Dokl., 7, 1242-1246 (1966) · Zbl 0161.11304 |
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