Algebraic models for probability measures on Banach spaces

1976 ◽  
Vol 8 (2) ◽  
pp. 215-217
Author(s):  
A. T. Bharucha-Reid
Keyword(s):  
Banach Spaces ◽  
Probability Measures ◽  
Algebraic Models

scholarly journals Fixed point theorems for metric spaces with a conical geodesic bicombing

2017 ◽  
Vol 38 (5) ◽  
pp. 1642-1657 ◽  
Author(s):  
GIULIANO BASSO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probability Measures

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a $1$-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.

scholarly journals Moments of probability measures on a group

1981 ◽  
Vol 4 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Herbert Heyer
Keyword(s):  
Topological Group ◽  
Banach Spaces ◽  
Lie Groups ◽  
Finite Groups ◽  
Lie Group ◽  
Probability Measures ◽  
Moment Conditions ◽  
New Developments ◽  
Large Numbers ◽  
Special Cases

New developments and results in the theory of expectatiors and variances for random variables with range in a topological group are presented in the following order (i) Introduction (2) Basic notions (3) The three series theorem in Banach spaces (4) Moment Conditions (5) Expectations and variances (6) A general three series theorem (7) The special cases of finite groups and Lie groups (8)The strong laws of large numbers on a Lie group (9) Further studies on moments of probability measures.

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