We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain the value ∞. We show that this is true i...

the probability density functions fitting to the discrete probability functions has always been needed, and very important. this paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. the main key in these fittings is the use of the derivative concept and common differential ...

The distribution theory for reward functions on semi-Markov processes has been of interest since the early 1960s. The relevant asymptotic distribution theory has been satisfactorily developed. On the other hand, it has been noticed that it is difficult to find exact distribution results which lead to the effective computation of such distributions. Note that there is no satisfactory exact distr...

If f : [0, 1] → R is strictly increasing and continuous define Tfx = f(x) (mod 1). A transformation T̃ : [0, 1] → [0, 1] is called ε-close to Tf , if T̃ x = f̃(x) (mod 1) for a strictly increasing and continuous function f̃ : [0, 1] → R with ‖f̃ − f‖∞ < ε. It is proved that the topological pressure p(Tf , g) is lower semi-continuous, and an upper bound for the jumps up is given. Furthermore the cont...

This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, tog...