On differentiability of Peano type functions. II
Measure preserving analytic diffeomorphisms of countable dense sets in and
On differentiability of Peano type functions
Algebras of Borel measurable functions
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Sierpiński's hierarchy and locally Lipschitz functions
Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and then f ○ g ∈ for every if and only if f is continuous on I, where stands for the αth class in Baire’s classification of Borel measurable functions. We shall prove that for the classes in Sierpiński’s classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz...
A short proof of decomposition of strongly reduced martingales
An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals
Page 1