for all f ∈ Cb(R ) and λ is continuous in the sense that if {fj} ∞ j=1 is a sequence of bounded continuous functions on R which is uniformly bounded and converges uniformly on compact subsets of R to a bounded continuous function f , then {λ(fj)} ∞ j=1 converges to λ(f). If f is any bounded continuous function on R, then there is a sequence {fj} ∞ j=1 of continuous functions on R n such that ea...

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...

Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary topological group.