The axiomatic melting point. Teaching probability theory in Prague during the 1930's.
The Baire and Borel measure
The Banach–Mazur game and σ-porosity
It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.
The Banach-Saks property and Haar null sets
A characterization of Haar null sets in the sense of Christensen is given. Using it, we show that if the dual of a Banach space has the Banach-Saks property, then closed and convex subsets of with empty interior are Haar null.
The Banach-Tarski Paradox
The Beta(p,1) extensions of the random (uniform) Cantor sets
Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal is greater...
The Bochner and the monotone integrals with respect to a nuclear-valued finitely additive measure
The Bochner-Kolmogorov extension theorem for semispectral measures
The Borel structure of the collections of sub-self-similar sets and super-self-similar sets.
The Bourbaki integral as maximal integral
The Box Dimension of Completely Invariant Subsets for Expanding Piecewise Monotonic Transformations.
The box-counting dimension for geometrically finite Kleinian groups
We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the...
The Brooks-Jewett theorem for -triangular functions
The Brooks-Jewett theorem for -triangular functions on difference posets and orthoalgebras
The cancellation law for pseudo-convolution
Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms and , of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.
The capacity of parabolic Julia sets.
The cardinality of the set of invariant means on a locally compact topological semigroup
The category of disintegration
The Cauchy-Riemann operator in infinite dimensional spaces.
The centralizer of ergodic theory group extensions