Measure
The terms ``measure,'' ``measurable,'' etc., have very precise technical definitions (usually involving SigmaAlgebras) which makes them a little difficult to understand. However, the technical nature of thedefinitions is extremely important, since it gives a firm footing to concepts which are the basis for much ofAnalysis (including some of the slippery underpinnings of Calculus).
For example, every definition of an Integral is based on a particular measure: the Riemann Integral is based onJordan Measure, and the Lebesgue Integral is based on Lebesgue Measure. The study of measures and theirapplication to Integration is known as Measure Theory.
A measure is formally defined as a Nonnegative Map 
(the reals) such that 
and, if
is a Countable Sequence in 
and the are pairwise Disjoint, then
If, in addition,
, then 
is said to be a Probability Measure. A measure may also be defined on Sets other than those in the Sigma Algebra . By adding to all sets to which assigns measure zero, we again obtain a Sigma Algebra and call this the ``completion'' of with respect to . Thus, the completion of a Sigma Algebra is the smallest Sigma Algebra containing andall sets of measure zero.
- Euler Number
- Euler Parameters
- Euler-Poincaré Characteristic
- Euler Polyhedral Formula
- Euler Polynomial
- Euler Polynomial Identity
- Euler Power Conjecture
- Euler Product
- Euler Pseudoprime
- Euler Quartic Conjecture
- Euler's 6n+1 Theorem
- Euler's Addition Theorem
- Euler's Circle
- Euler's Conjecture
- Euler's Criterion
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem