Measures on Boolean algebras

Measures on Boolean algebras

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.

Strictly positive measures on Boolean algebras

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characte...

On possibility and probability measures in finite Boolean algebras

A strong log-concavity property for measures on Boolean algebras

We introduce the antipodal pairs property for probability measures on finite Boolean algebras and prove that conditional versions imply strong forms of log-concavity. We give several applications of this fact, including improvements of some results of Wagner [15]; a new proof of a theorem of Liggett [9] stating that ultra-log-concavity of sequences is preserved by convolutions; and some progres...

On Poset Boolean Algebras

Let 〈P,≤〉 be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P ) is {xp : p ∈ P}, and the set of relations is {xp ·xq = xp : p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G,≤G〉 is well-founded. A wellgenerated algebra is superatomic. Theorem 1 Let 〈P,≤〉 be a...