Category:Measure Theory Definitions

A

• Additive function
• Additive set function
• Algebra
• Algebra (disambiguation)
• Algebra (measure theory)
• Algebra of sets
• Algebras of sets

B

• Borel sigma-algebra
• Borel sigma-algebra generated by
• Borel sigma-algebra of the real line

C

• Class of smooth real-valued functions on R-n
• Class of smooth real-valued functions on R-n/Structure
• Classes of continuously differentiable functions
• Complementation
• Countably additive set function

D

• D-system
• Derivative
• Dynkin system
• Dynkin system generated by
• Dynkin system/Definition 1
• Dynkin system/Definition 2
• Dynkin systems

E

• Extended real value
• Extended real valued
• Extended real values

F

• Finitely additive set function
• Function terminology

G

• Generator
• Generator (sigma-algebra)

H

• Hereditary
• Hereditary (measure theory)
• Hereditary class of sets
• Hereditary set system
• Hereditary sigma-ring
• Hereditary sigma-ring generated by
• Hereditary system

H cont.

• Hereditary system generated by
• Hereditary system of sets

I

• Index of common sigma-algebras
• Integral
• Integral (measure theory)
• Integral of a positive function (measure theory)
• Integral of a positive function (measure theory)/Definition
• Integral of a simple function (measure theory)
• Integral of a simple function (measure theory)/Definition

L

• Lebesgue measure
• Liminf (sequence of sets)
• Limit of increasing sequence of sets
• Limsup (sequence of sets)
• Limsup and liminf (sequence of sets)

M

• Measurable function
• Measurable functions
• Measurable map
• Measurable space
• Measure
• Measure space
• Min/max
• Minimum
• Minimum function
• Monotone
• Monotonic
• Monotonic set function
• Mu*-measurable set

O

• Outer splicing set
• Outer-measure
• Outer-measure/Definition

P

• P-system
• Positive and negative parts of a function
• Pre-image sigma-algebra
• Pre-image sigma-algebra/Definition
• Pre-measurable space
• Pre-measure

P cont.

• Pre-measure on a semi-ring
• Pre-measure space
• Pre-measure/New page
• Premeasurable space
• Premeasurable space/Definition
• Probability function
• Probability measure
• Probability space

R

• Random variable
• Random variables
• Real-valued function
• Ring (measure theory)
• Ring generated by
• Ring of sets
• Ring of sets/Definition

S

• Semi-ring (measure theory)
• Semi-ring of half-closed-half-open intervals
• Semi-ring of sets
• Semi-ring of sets/Definition
• Semiring (measure theory)
• Semiring of sets
• Set function
• Sigma-algebra
• Sigma-algebra generated by
• Sigma-algebra/Definition
• Sigma-algebras
• Sigma-field
• Sigma-ring
• Simple function (measure theory)
• Simple function (measure theory)/Definition
• Simple function under-approximation to a numerical function
• Subtractive set function
• Symmetric difference

T

• Trace sigma-algebra
• Trivial
• Types of set algebras