De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those ...

In 1934 Sierpiński [5] proved that every function from a countable family X of continuous functions f : [0, 1] → [0, 1] can be obtained as a composition of four such functions. These four functions are said to generate the aforementioned family. The sequence X is not necessarily closed under composition, so it may be more precise to say that these four functions generate a semigroup containing ...

We investigate which event structures can be denoted by means of closed CCS CSP expressions. Working up to isomorphism we find that all denotable event structures are bundle event structures, upon adding an infinitary parallel composition all bundle event structures are denotable, without it every finite bundle event structure can be denoted, as well as every countable prime event structure wit...

The symmetric inverse semigroup I(X) on a set X is the collection of all partial bijections between subsets with composition as algebraic operation. We study minimal Hausdorff topology I(X). present some characterizations it. When countable such Polish.

‎For any archimedean$f$-ring $A$ with unit in whichbreak$awedge‎ ‎(1-a)leq 0$ for all $ain A$‎, ‎the following are shown to be‎ ‎equivalent‎: ‎ ‎1‎. ‎$A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all‎ ‎integer-valued continuous functions on some frame $L$‎. 2‎. ‎$A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$‎ ‎of all integer-valued continuous functions‎, ‎in the usual se...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

‎for any archimedean$f$-ring $a$ with unit in whichbreak$awedge‎‎(1-a)leq 0$ for all $ain a$‎, ‎the following are shown to be‎‎equivalent‎:‎‎1‎. ‎$a$ is isomorphic to the $l$-ring ${mathfrak z}l$ of all‎‎integer-valued continuous functions on some frame $l$‎. 2‎. ‎$a$ is a homomorphic image of the $l$-ring $c_{bbb z}(x)$‎‎of all integer-valued continuous functions‎, ‎in the usual sense‎,‎on som...