Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon and Maurice Fréchet, among others.

But as Cormack remembered later, he had to find the solution himself since it was only in 1972 that he learned of the work of Radon, by chance.

Johann Karl August Radon ( 16 December 1887 – 25 May 1956 ) was an Austrian mathematician.

Radon was born in Tetschen, Bohemia, Austria-Hungary, now Děčín, Czech Republic.

Radon, as Curt C. Christian described him in 1987 at the occasion of the unveiling of his brass bust at the University of Vienna, was a friendly, good-natured man, highly esteemed by students and colleagues alike, a noble personality.

The transform was introduced by Johann Radon ( 1917 ), who also provided a formula for the inverse transform.

The company's former headquarters, the Avaz Business Center ( Former Oslobođenje Building ), was converted into a highrise hotel, Radon Plaza Hotel ( based on the owner's last name Radončić ).

The mathematical basis for tomographic imaging was laid down by Johann Radon.

Subchapter III of the TSCA, " Indoor Radon Abatement ," was enacted by the U. S. Congress in 1988 under PL 100-551.

The first full-scale tour of Steve Mackay and the Radon Ensemble was mounted in July 2003 ; with a percussion-heavy lineup featured bassist Marlon Kasberg ( Liquorball ), drummer Sam Lohman ( Nimrod 36 ), multi-instrumentalist Travis McAlister ( Nequaquam Vacuum ), scrap percussionist and vocalist Noah Mickens ( also Nequaquam Vacuum ), and drummer and band leader Scott Nydegger ( Sikhara ).

* He is possibly the first to make use of the so called Radon – Riesz property.

This is the first numerical inversion of the Radon transform and it gives the lie to the often made statement that computed tomography would be impossible without computers.

Scott Nydegger from the small record label and noise collective, Radon, disproved the rumor by contacting Mackay and arranging to release his first solo recordings.

When the measure space is furthermore sigma-finite then L < sup >∞</ sup >( μ ) is in turn dual to L < sup > 1 </ sup >( μ ), which by the Radon – Nikodym theorem is identified with the set of all countably additive μ-a. c. measures.

* Measure algebra: A Banach algebra consisting of all Radon measures on some locally compact group, where the product of two measures is given by convolution.

Radon is a colorless and odorless gas, and therefore not detectable by human senses alone.

Radon can be oxidized by a few powerful oxidizing agents such as fluorine, thus forming radon fluoride.

The mathematical theory behind the Tomographic reconstruction dates back to 1917 where the invention of Radon Transform by an Austrian mathematician Johann Radon.

Radon mitigation methods include sealing concrete slab floors, basement foundations, water drainage systems, or by increasing ventilation.

** Existence of a conditional expectation function is determined by the Radon – Nikodym theorem, a sufficient condition is that the ( unconditional ) expected value for X exist.

The Radon transform, Rƒ, is a function defined on the space of straight lines L in R < sup > 2 </ sup > by the line integral along each such line:

It follows that the quantities ( α, s ) can be considered as coordinates on the space of all lines in R < sup > 2 </ sup >, and the Radon transform can be expressed in these coordinates by

It is also possible to generalize the Radon transform still further by integrating instead over k-dimensional affine subspaces of R < sup > n </ sup >.

Beginning with a function g on the space Σ < sub > n </ sub >, the dual Radon transform is the function R < sup >∗</ sup > g on R < sup > n </ sup > defined by

Concretely, for the two-dimensional Radon transform, the dual transform is given by

The Radon transform in n dimensions can be inverted by the formula

( It is possible to extend the theory of Radon measures to non-Hausdorff spaces, essentially by replacing the word " compact " by " closed compact " everywhere.

Conversely, by the Riesz representation theorem, each positive linear form on arises as integration with respect to a Radon measure and is thus a continuous positive linear form on.

Radon decay produces alpha particles ( responsible by helium emissions in HL spectrum ) and radioactive elements such as polonium.

In 2003, the Austrian Academy of Sciences founded an Institute for Computational and Applied Mathematics and named it after Johann Radon ( see External link below ).

Lebesgue – Stieltjes integrals, named for Henri Leon Lebesgue and Thomas Joannes Stieltjes, are also known as Lebesgue – Radon integrals or just Radon integrals, after Johann Radon, to whom much of the theory is due.

In mathematics, the Radon transform in two dimensions, named after the Austrian mathematician Johann Radon, is the integral transform consisting of the integral of a function over straight lines.

In mathematics ( specifically, measure theory ), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.

In geometry, Radon's theorem on convex sets, named after Johann Radon, states that any set of d + 2 points in R < sup > d </ sup > can be partitioned into two ( disjoint ) sets whose convex hulls intersect.

Radon is an invisible, radioactive atomic gas that results from the radioactive decay of radium, which may be found in rock formations beneath buildings or in certain building materials themselves.

Radon exposure is considered the leading cause of lung cancer in non-smokers.

Radon is one of the densest gases at room temperature and is the densest of the noble gases.

Radon is a member of the zero-valence elements that are called noble gases.

Radon is sparingly soluble in water, but more soluble than lighter noble gases.

Radon gas poses significant health concerns, and is the number two cause of lung cancer in the US behind smoking.

Radon is one of the densest substances that remains a gas under normal conditions.

Radon is a heavy gas and thus will tend to accumulate at the floor level.

For example, miners in Newfoundland had been exposed to Radon gas, and although the company ( and the Canadian government ) were aware of the health risks, it did not take any action.

In 1987, the New Scientist reported that Chagford contained " the most radioactive loo in the world ", a reference to the high levels of Radon gas in this granite area.

The detectors were installed inside a sealed copper box flushed with highly pure ( HP ) Nitrogen in order to insulate the detectors from air that contains the Radon, a radioactive gas, in trace.

Radon gas in homes is the largest source of radiation dose for most individuals and it is generally advised that the concentration be kept below 150 Bq / m³ ( 4 pCi / L ).

* Radon gas exposure in individuals ' homes.