In the context of functional analysis and measure theory, a function is said to be **weakly measurable** if it behaves well with respect to the weak topology on a space of functions. The concept is particularly relevant in the study of Banach and Hilbert spaces.
"Webbed space" typically refers to a concept within web development and design, but the term can be context-dependent. Here are a couple of interpretations: 1. **Web Design Context**: In web design, "webbed space" may refer to the layout and structure of a website that uses a grid or modular format, creating interconnected sections or modules—akin to a web. This can involve organizing content in a way that allows for easy navigation and interaction across different areas of the site.
The Weierstrass M-test is a criterion used in analysis to establish the uniform convergence of a series of functions. More specifically, it provides a way to determine whether a series of functions converges uniformly to a limit function on a certain domain. ### Statement of the Weierstrass M-test Consider a series of functions \( \sum_{n=1}^{\infty} f_n(x) \) defined on a set \( D \).
The term "weighted space" can refer to different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Weighted Function Spaces in Mathematics**: In functional analysis, weighted spaces refer to function spaces where functions are multiplied by a weight function. This weight function modifies how lengths, integrals, or norms are calculated, which can be particularly useful in various theoretical contexts, such as studying convergence, boundedness, or compactness of operators between these spaces.
Wetzel's problem is a question in mathematical logic and set theory, specifically related to the properties of functions and sets. It was posed by the mathematician David Wetzel in the context of exploring the properties of certain types of functions.
The Wiener series is a mathematical concept used primarily in the field of stochastic processes, particularly in the study of Brownian motion and other continuous-time stochastic processes. It provides a way to represent certain types of stochastic processes as an infinite series of orthogonal functions. ### Key Features of Wiener Series: 1. **Representation of Brownian Motion**: The Wiener series is often used to express Brownian motion (or Wiener process) in terms of a stochastic integral with respect to a Wiener process.