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A substitute of the expected value

Urbanik K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

285-297

To every probability measure /.t there corresponds a subspace X(u) generated by convex linear combinations of independent random variables X_1,X_2,... with the same probability distribution u and closed under the convergence in probability. The purpose of this paper is a construction of generalized expected values of u based on the space X (u).

Moments and Generalized Convolutions. III

Urbanik K.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 1

153--169

The paper deals with some uniqueness and characterization theorems for probability measures and generalized convolutions in terms of negative moments.