Orthogonal Measures: An Example
Maharam, Dorothy
Ann. Probab., Tome 10 (1982) no. 4, p. 879-880 / Harvested from Project Euclid
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A family $\{\mu_\alpha\}$ of measures on a $\sigma$-field $\mathscr{B}$ on a space $X$ is "uniformly orthogonal" means that for each $\alpha, \exists H_\alpha \in \mathscr{B}$ such that $\mu_\alpha (X - H_\alpha) = \mu_\beta(H_\alpha) = 0$ if $\beta \neq \alpha$. Assuming $CH$, an example is given of an orthogonal family of measures on the Borel sets of $I^2$ such that no uncountable subfamily is uniformly orthogonal. Assuming $\sim CH + MA$, such an uncountable family obviously exists.
Publié le : 1982-08-14
Classification:  Orthogonal measures,  uniformly orthogonal measures,  28A10 
@article{1176993803,
     author = {Maharam, Dorothy},
     title = {Orthogonal Measures: An Example},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 879-880},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993803}
}

Maharam, Dorothy. Orthogonal Measures: An Example. Ann. Probab., Tome 10 (1982) no. 4, pp.  879-880. http://gdmltest.u-ga.fr/item/1176993803/