# Strong laws of large numbers in certain linear spaces

Annales de l'institut Fourier (1974)

- Volume: 24, Issue: 2, page 205-223
- ISSN: 0373-0956

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topWoyczynski, Wojbor A.. "Strong laws of large numbers in certain linear spaces." Annales de l'institut Fourier 24.2 (1974): 205-223. <http://eudml.org/doc/74174>.

@article{Woyczynski1974,

abstract = {In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous $F$-norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.},

author = {Woyczynski, Wojbor A.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {2},

pages = {205-223},

publisher = {Association des Annales de l'Institut Fourier},

title = {Strong laws of large numbers in certain linear spaces},

url = {http://eudml.org/doc/74174},

volume = {24},

year = {1974},

}

TY - JOUR

AU - Woyczynski, Wojbor A.

TI - Strong laws of large numbers in certain linear spaces

JO - Annales de l'institut Fourier

PY - 1974

PB - Association des Annales de l'Institut Fourier

VL - 24

IS - 2

SP - 205

EP - 223

AB - In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous $F$-norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.

LA - eng

UR - http://eudml.org/doc/74174

ER -

## References

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- [2] A. BECK and D. P. GIESY, P-uniform convergence and a vector-valued strong laws of large numbers, Trans. Amer. Math. Soc., 147 (1970), 541-559. Zbl0198.51006MR41 #7728
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- [5] J. HOFFMANN-JORGENSEN, Sums of independent Banach space valued random variables, Aarhus Universitet, Matematisk Institut, Preprint Series, 1972/1973, No 15, 1-89.
- [6] J.-P. KAHANE, Some random series of functions, Heath, Lexington, 1968. Zbl0192.53801MR40 #8095
- [7] V. V. PETROV, Sums of independent random variables, Nauka, Moscow, 1972 (in Russian). Zbl0288.60050MR46 #4606
- [8] V. V. PETROV, On the rate of growth of dependent random variables, Teor. Probability Appl., 18 (1973), 358-361. Zbl0295.60020MR47 #7792
- [9] P. RÉVÉSZ, The laws of large numbers, Academic Press, New York, 1968. Zbl0203.50403MR39 #6391
- [10] S. ROLEWICZ, Metric linear spaces, PWN, Warsaw, 1972. Zbl0226.46001MR55 #10993
- [11] W. A. WOYCZYŃSKI, Random series and laws of large numbers in some Banach spaces, Theor. Probability Appl., 18 (1973), 361-367. Zbl0324.60041MR47 #7793

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