Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

In addition, Jurema ( Mimosa tenuiflora ) shows evidence of DMT content: the pink layer in the inner rootbark of this small tree contains a high concentration of N, N-DMT.

In mathematical analysis, an isomorphism between two Hilbert spaces is a bijection preserving addition, scalar multiplication, and inner product.

In addition, the inner membrane is rich in an unusual phospholipid, cardiolipin.

In addition, there is a membrane potential across the inner membrane, formed by the action of the enzymes of the electron transport chain.

Targeting to the outer membrane, intermembrane space, and inner membrane often requires another signal sequence in addition to the matrix targeting sequence.

Random vectors can be subjected to the same kinds of algebraic operations as can non-random vectors: addition, subtraction, multiplication by a scalar, and the taking of inner products.

The inner structure of a commutative ring is determined by considering its ideals, i. e. nonempty subsets that are closed under multiplication with arbitrary ring elements and addition: for all r in R, i and j in I, both ri and i + j are required to be in I.

A $ 2 billion project to redevelop Melbourne's derelict Docklands area to include a new football stadium was also undertaken, in addition to the large CityLink project, a project resurrected from the 1969 Melbourne Transportation Plan, aimed at linking Melbourne's freeways, easing traffic problems in the inner city, and reducing commuting times from the outer suburbs to the CBD.

In addition to its familiar geometric structure, with isomorphisms that are isometries with respect to the usual inner product, the plane may be viewed at various other levels of abstraction.

In the process, it binds four protons from the inner aqueous phase to make water, and in addition translocates four protons across the membrane, helping to establish a transmembrane difference of proton electrochemical potential that the ATP synthase then uses to synthesize ATP.

A new addition to the Nome facility in 2005 was a concrete barge ramp located inside the inner harbor just west of the Snake River entrance.

It offers camps during the summer for locals, in addition to a camp for inner city kids.

In addition to opposing jaws, living gnathostomes also have teeth, paired appendages, and a horizontal semicircular canal of the inner ear, along with physiological and cellular anatomical characters such as the myelin sheathes of neurons.

The addition of small quantities of phosphate ion and increasing the pH slightly both assist in greatly reducing plumbo-solvency by creating insoluble lead salts on the inner surfaces of the pipes.

* Cancellation of signal: In addition, many AM stations, including but not limited to the clear channel stations, often experience cancellation of their own signals within the inner and outer fringes of their normal groundwave coverage areas at nighttime due to the stations ' individual skywave signals reaching the listeners ' receivers at or near equal strength to the stations ' individual groundwave signals ; this phenomenon is very similar to the multipath interference experienced on FM Radio in the VHF band within mountainous regions and urban areas due to signals bouncing off of mountains, buildings, and other structures, except that the groundwave-skywave cancellation occurs almost exclusively at nighttime when skywave propagation is present.

Hunter contributes to many charities, including the " Torii Hunter Project Education Initiative ," which provides college scholarships to students in California, Arkansas, Nevada and Minnesota, the Andre Agassi College Preparatory Academy in Las Vegas, a partnership with Major League Baseball to help maintain and improve baseball diamonds in inner cities, the Big Brothers and the Prostate Cancer Foundation, and in addition, Hunter helped fund construction of a youth softball field in Placentia, California in 2008.

In addition to the inner city shopping centres, large UK conurbations will also have large out-of-town " regional malls " such as Meadowhall, Sheffield serving South Yorkshire, the Trafford Centre in Greater Manchester and Bluewater in Kent.

Towards the end of inhalation the bellows bottoms out and activates an addition valve, in much the way that a regulator diaphragm activates the demand valve, to make up the gas discharged by the inner bellows.

In reptiles and birds, the ciliary body touches the lens with a number of pads on its inner surface, in addition to the zonular fibres.

In addition to these water coasters, the New Braunfels park now boasts over 3 miles ( 5 km ) of inner tube rides, 7 water playgrounds for children, 17 water slides, 9 tube chutes, and the world's first surfing machine ( Boogie Bahn, which is used by both professionals and casual visitors ).

In the second formula, the inner summation in the right hand side is only extended over indices within bounds, 0 ≤ i ≤ m and 0 ≤ j ≤ n. Alternative expressions of addition and multiplication, without using explicit bounds in the sums, are as follows:

The central ring canal, in addition to connecting the radial canals to each other and to the stone canal, also has a number of other specialised structures on the inner surface.

In addition, dirt particles can be held onto a soiled surface by sticky substances or by the surface tension of liquids, including liquid greases.

In addition, there were difficulties with the flow and spreading of the foam mixture over the mold surface, trouble with lack of gel strength in the rising foam, and problems of splits.

It is thought that, in addition to exuding onto the surface of the tree, amber resin also originally flowed into hollow cavities or cracks within trees, thereby leading to the development of large lumps of amber of irregular form.

In addition, cutting operations can smear the lead globules over the surface.

The analogy in the case of rotating bucket is that the element of water surface will " slide " up or down the surface unless the normal to the surface aligns with the vector resultant formed by the vector addition F < sub > g </ sub > + F < sub > Cfgl </ sub >.

This can be accomplished by the addition of salt to a suspension or changing the pH of a suspension to effectively neutralize or " screen " the surface charge of the particles in suspension.

Another factor in addition to the packing shape and surface area that affects the performance of random or structured packing is the liquid and vapor distribution entering the packed bed.

Functionalization is the addition of functional groups onto the surface of a material by chemical synthesis methods.

In addition, functional groups are used to covalently link functional molecules to the surface of chemical and biochemical devices such as microarrays and microelectromechanical systems.

In addition, many localities rely on surface sources, making users vulnerable to agricultural runoff and livestock waste, which seep gradually downward from the surface.

In addition, non-polar interactions are made between protein side-chains and the deoxyribose groups, and an arginine side-chain intercalates into the DNA minor groove at all 14 sites where it faces the octamer surface.

This characteristic has made it a useful addition to no-till and low-till farming practices which attempt to maximise the erosion-prevention benefits of keeping organic matter and farming residues present on the soil surface through the year.

In addition, the plastic sleeves can develop kinks or creases in the surface, which will scratch away at the emulsion during handling.

In addition, miniature engines suffer from an adverse surface to volume ratio ; the relatively large surface area transfers away what little heat is generated in the small combustion volume resulting in quenching and low efficiency.

In addition, since 2004, new glaciers have formed on the crater wall above Crater Glacier feeding rock and ice onto its surface below ; there are two rock glaciers to the north of the eastern lobe of Crater Glacier.

In addition to Seurat, the roots of cubism are to be found in the two distinct tendencies of Cézanne's later work: first his breaking of the painted surface into small multifaceted areas of paint, thereby emphasizing the plural viewpoint given by binocular vision, and second his interest in the simplification of natural forms into cylinders, spheres, and cones.

The rate of initial reaction ( up to 24 hours ) of the cement on addition of water is directly proportional to the specific surface area.

In addition to their small size, the surface normal operation of VCSOAs leads to a number of advantages, including low power consumption, low noise figure, polarization insensitive gain, and the ability to fabricate high fill factor two-dimensional arrays on a single semiconductor chip.

In addition, if the plane of the reflecting surface is not aligned with the plane of propagation of the wave, the polarization of the two parts is altered.