and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...

A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss ...

In 1900, Dorn discovered the emanation in the uranium series that eventually became the well-known gas Rn. From 1900 through 1908, it was demonstrated that Rn is a radioactive gas found in tap water, highly condensable at low temperatures with a halflife of approximately 3.7 days and can be collected on charcoal by adsorption. Although, radon was discovered in 1900, the effects of prolonged exp...

The ability to monitor radon-flux density continuously is of great value in elucidating radon-transport mechanisms. Intercomparisons of two radon-flux measurement systems were conducted in one of the two test structures operated by Colorado State University (CSU). Systems used by the U.S. Department of Energy Grand Junction Projects Office (GJPO) Radon Laboratory and the CSU investigators are s...

Based on a mathematical analysis involving Radon measure explicit formulars of continuous (integral) wavelet transformations are given and further used to direct how to use rotational wavelets in edge detection.

We show that in the one-dimensional case the weighted Hardy–Littlewood maximal operator Mμ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.

We performed both a laboratory and a field intercomparison of two novel glass-based retrospective radon detectors previously used in major radon case-control studies performed in Missouri and Iowa. The new detectors estimate retrospective residential radon exposure from the accumulation of a long-lived radon decay product, (210)Pb, in glass. The detectors use track registration material in dire...

We show that the Hilger derivative on time scales is a special case of the Radon–Nikodym derivative with respect to the natural measure associated with every time scale. Moreover, we show that the concept of delta absolute continuity agrees with the one from measure theory in this context.

We study the absolute continuity of the image measure of the canonical Poisson probability measure under nonlinear shifts. The Radon-Nykodim density function is expressed using a Carleman-Fredholm determinant and a divergence operator. Results are obtained for non-necessarily invertible transformations, under almost-sure differentiability hypothesis.

This paper is devoted to the proof of two related results. The first one asserts that if μ is a Radon measure in R satisfying lim sup r→0 μ(B(x, r)) r > 0 and ∫ 1