# On some definition of expectation of random element in metric space

Annales UMCS, Mathematica (2009)

- Volume: 63, Issue: 1, page 39-48
- ISSN: 2083-7402

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topArtur Bator, and Wiesław Zięba. "On some definition of expectation of random element in metric space." Annales UMCS, Mathematica 63.1 (2009): 39-48. <http://eudml.org/doc/268117>.

@article{ArturBator2009,

abstract = {We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.},

author = {Artur Bator, Wiesław Zięba},

journal = {Annales UMCS, Mathematica},

keywords = {Convex combination; metric space; Banach space; martingale; amart; convex combination},

language = {eng},

number = {1},

pages = {39-48},

title = {On some definition of expectation of random element in metric space},

url = {http://eudml.org/doc/268117},

volume = {63},

year = {2009},

}

TY - JOUR

AU - Artur Bator

AU - Wiesław Zięba

TI - On some definition of expectation of random element in metric space

JO - Annales UMCS, Mathematica

PY - 2009

VL - 63

IS - 1

SP - 39

EP - 48

AB - We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.

LA - eng

KW - Convex combination; metric space; Banach space; martingale; amart; convex combination

UR - http://eudml.org/doc/268117

ER -

## References

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