“Fatou's Theorems”的概念、定义、习题解题方法及翻译-数学辞典

单词

Fatou's Theorems

释义

Fatou's Theorems

Let be Lebesgue Integrable and let

(1)

be the corresponding Poisson Integral. Then Almost Everywhere in

(2)

Let

(3)

be regular for

, and let the integral

(4)

be bounded for

. This condition is equivalent to the convergence of

(5)

Then almost everywhere in

(6)

Furthermore,

is measurable,

is Lebesgue Integrable, and the FourierSeries of

is given by writing

References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 274, 1975.

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